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Selina solutions for Concise Mathematics Class 10 ICSE chapter 17 - Circles [Latest edition]

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Chapter 17: Circles

Exercise 17(A)Exercise 17(B)Exercise 17(C)

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 17 Circles Exercise 17(A) [Pages 257 - 262]

Exercise 17(A) | Q 1 | Page 257

In the given figure, O is the centre of the circle. ∠OAB and ∠OCB are 30° and 40°
respectively. Find  ∠AOC . Show your steps of working.

Exercise 17(A) | Q 2 | Page 257

In the figure, ∠BAD  = 65° , ∠ABD = 70° , ∠BDC = 45°
(i) Prove that AC is a diameter of the circle
(ii) Find ∠ACB

Exercise 17(A) | Q 3 | Page 257

Given O is the centre of the circle and ∠AOB  = 70°. Calculate the value of:
(i)  ∠OCA  .
(ii) ∠OCA  .

Exercise 17(A) | Q 4.1 | Page 257

In the following figures, O is the centre of the circle. Find the values of a, b and c.

Exercise 17(A) | Q 4.2 | Page 257

In the following figures, O is the centre of the circle. Find the values of a, b and c.

Exercise 17(A) | Q 5.1 | Page 258

In the following figures, O is the centre of the circle. Find the value of a, b, c and d.

Exercise 17(A) | Q 5.2 | Page 258

In the following figures, O is the centre of the circle. Find the values of a, b, c and d.

Exercise 17(A) | Q 5.3 | Page 258

In the following figures, O is the centre of the circle. Find the values of a, b, c and d

.

Exercise 17(A) | Q 5.4 | Page 258

In the following figures, O is the centre of the circle. Find the values of a, b, c and d.

Exercise 17(A) | Q 6 | Page 258

In the figure, AB is common chord of the two circle. If AC and AD are diameters; prove that D,
B and C are in a straight line. O1 and O2 are the centres of two circles.

Exercise 17(A) | Q 7.1 | Page 258

In the figure, given below, find: ∠BCD,  Show steps of your working .

Exercise 17(A) | Q 7.2 | Page 258

In the figure, given below, find: ∠ ADC show steps of your working.

Exercise 17(A) | Q 7.3 | Page 258

In the figure, given below, find: ∠ ABC Show steps of your working.

Exercise 17(A) | Q 8 | Page 258

In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; Find:
(i) ∠ACB,  (ii) ∠OBC,  (iii) ∠OAB,  (iv) ∠CBA.

Exercise 17(A) | Q 9 | Page 258

Calculate:
(i) ∠CDB, (ii) ∠ABC, (iii) ∠ACB

Exercise 17(A) | Q 10 | Page 258

In the figure, given below, ABCD is a cyclic quadrilateral in which ∠BAD = 75°; ∠ABD = 58°

(i) ∠BDC, (ii) ∠BCD, (iii) ∠BCA.

Exercise 17(A) | Q 11 | Page 258

In the following figure, O is centre of the circle and ΔABC is equilateral.

Exercise 17(A) | Q 12 | Page 258

Given: ∠CAB = 75° and ∠CBA = 50°. Find the value of ∠DAB + ∠ABD.

Exercise 17(A) | Q 13 | Page 258

ABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°; find ∠ BAC.

Exercise 17(A) | Q 14 | Page 258

In the figure, given below, AOB is a diameter of the circle and ∠AOC = 110°. Find ∠BDC.

Exercise 17(A) | Q 15 | Page 258

In the following figure, O is the centre of the circle,
∠AOB = 60° and ∠BDC = 100° Find ∠OBC.

Exercise 17(A) | Q 16.1 | Page 259

ABCD is a cyclic quadrilateral in which  ∠DAC = 27° ; ∠DBA = 50° and ∠ADB = 33°. Calculate : ∠DBC,

Exercise 17(A) | Q 16.2 | Page 259

In ABCD is a cyclic quadrilateral in which ∠ DAC = 27° , ∠ DBA = 50° and ∠ ADB = 33°. Calculate ∠ DCB.

Exercise 17(A) | Q 16.3 | Page 259

In ABCD is a cyclic quadrilateral in which ∠ DAC = 27° , ∠ DBA = 50° and ∠ ADB = 33°. Calculate ∠ CAB.

Exercise 17(A) | Q 17.1 | Page 259

In the figure given below, AB and CD are straight lines through the centre O of a circle. If ∠AOC
= 80° and ∠CDE = 40°, Find the number of degrees in:
∠ DCE .

Exercise 17(A) | Q 17.2 | Page 259

In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, Find the number of degrees in : ∠ ABC .

Exercise 17(A) | Q 18 | Page 259

In the given figure, AC is a diameter of a circle, whose centre is O. A circle is described on AO
as diameter. AE, a chord of the larger circle, intersects the smaller circle at B. prove that AB =
BE.

Exercise 17(A) | Q 19.1 | Page 259

In the following figure,

If ∠BAD = 96°, find ∠BCD and ∠BFE.

Exercise 17(A) | Q 19.2 | Page 259

In the following figure, Prove that AD is parallel to FE.

Exercise 17(A) | Q 19.3 | Page 259

ABCD is a parallelogram. A circle through vertices A and B meets side BC at point P and side AD at point Q. Show that quadrilateral PCDQ is cyclic.

Exercise 17(A) | Q 20.1 | Page 259

Prove that:
the parallelogram, inscribed in a circle, is a rectangle.

Exercise 17(A) | Q 20.2 | Page 259

Prove that:
the rhombus, inscribed in a circle, is a square.

Exercise 17(A) | Q 21 | Page 259

In the following figure AB = AC. Prove that DECB is an isosceles trapezium.

Exercise 17(A) | Q 22 | Page 259

Two circles intersect at P and Q. through P diameter PA and PB of the two circles are drawn.
Show that the points A, Q and B are collinear.

Exercise 17(A) | Q 23.1 | Page 259

The figure given below, shows a Circle with centre O.
Given: ∠AOC = a and ∠ABC = b.

Find the relationship between a and b

Exercise 17(A) | Q 23.2 | Page 259

The figure given below, shows a circle with centre O. Given: ∠ AOC = a and  ∠ ABC = b.

Find the measure of angle OAB, if OABC is a parallelogram.

Exercise 17(A) | Q 24 | Page 259

Two chords AB and CD intersect at P inside the circle. Prove that the sum of the angles
subtended by the arcs AC and BD at the centre O is equal to twice the angle APC.

Exercise 17(A) | Q 25.1 | Page 259

In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.
Calculate:  ∠RNM,

Exercise 17(A) | Q 25.2 | Page 259

In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.

Calculate :  ∠ NRM

Exercise 17(A) | Q 26 | Page 259

In the figure, given alongside, AB ∥ CD and O is the centre of the circle. If ∠ADC = 25°; find

Exercise 17(A) | Q 27 | Page 259

Two circle intersect at P and Q. through P, a straight line APB is drawn to meet the circles in A
and B. Through Q, a straight line is drawn to meet the circles at C and D. prove that AC is
parallel to BD.

Exercise 17(A) | Q 28 | Page 260

ABCD is a cyclic quadrilateral in which AB and DC on being produced, meet at P such that PA
= PD. Prove that AD is parallel to BC.

Exercise 17(A) | Q 29.1 | Page 260

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines.
Find :  ∠PRB

Exercise 17(A) | Q 29.2 | Page 260

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find : ∠ PBR

Exercise 17(A) | Q 29.3 | Page 260

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find: ∠ BPR

Exercise 17(A) | Q 30 | Page 260

In the given figure, SP is bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = SR .

Exercise 17(A) | Q 31 | Page 260

In the figure, O is the centre of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

Exercise 17(A) | Q 32 | Page 260

In the figure, given below, P and Q are the centres of two circles intersecting at B and C ACD is a straight line. Calculate the numerical value of x .

Exercise 17(A) | Q 33.1 | Page 260

The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and lies on the circumference of the larger circle. Given that ∠APB = a°.

Calculate, in terms of a°, the value of : obtuse ∠AOB,

Exercise 17(A) | Q 33.2 | Page 260

The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and lies on the circumference of the larger circle.  Given that  ∠ APB = ao. Calculate, in terms of ao, the value of: ∠ ACB .

Exercise 17(A) | Q 33.3 | Page 260

The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and lies on the circumference of the larger circle.  iven that  ∠ APB = ao. Calculate, in terms of ao, the value of:  ∠ ADB.

Exercise 17(A) | Q 34 | Page 260

In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.

Exercise 17(A) | Q 35 | Page 260

In the given figure, A is the centre of the circle, ABCD is a parallelogram and CDE is a straight line.
Prove that : ∠BCD = 2∠ABE .

Exercise 17(A) | Q 36 | Page 260

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; Calculate:
(i) ∠DAB, (ii) ∠BDC

Exercise 17(A) | Q 37.1 | Page 260

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate : ∠ EBA

Exercise 17(A) | Q 37.2 | Page 260

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate : ∠ BCD.

Exercise 17(A) | Q 38.1 | Page 260
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate :  ∠DAB
Also show that the ΔAOD is an equilateral triangle .
Exercise 17(A) | Q 38.2 | Page 260

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.

Calculate : ∠DBA

Also, show that the Δ AOD is an equilateral triangle.

Exercise 17(A) | Q 38.3 | Page 261

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.

Calculate : ∠DBC

Also, show that the Δ AOD is an equilateral triangle.

Exercise 17(A) | Q 38.4 | Page 261

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.

Also, show that the Δ AOD is an equilateral triangle.

Exercise 17(A) | Q 39 | Page 261

In the given figure, I is the incentre of ΔABC. BI when produced meets the circumcircle of
ΔABC at D. ∠BAC = 55° and ∠ACB = 65°; calculate:
(i) ∠DCA, (ii) ∠DAC, (iii) ∠DCI, (iv) AIC

Exercise 17(A) | Q 40.1 | Page 261

A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that :

∠ABC = 2∠APQ,

Exercise 17(A) | Q 40.2 | Page 261

A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that:

∠ ACB = 2 ∠APR ,

Exercise 17(A) | Q 40.3 | Page 261

A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that:

angle "QPR" = 90^circ - 1/2  angle "BAC"

Exercise 17(A) | Q 41 | Page 261

Calculate the angles x, y and z if:
x /3= y/4 = z/5

Exercise 17(A) | Q 42 | Page 261

In the given figure, AB = AC = CD and ∠ADC = 38°. Calculate:
(i) Angle ABC
(ii) Angle BEC

Exercise 17(A) | Q 43 | Page 261

In the given figure, AC is a diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q and r in terms of x .

Exercise 17(A) | Q 44.1 | Page 261

In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. Angle ∠AOB = 80° and ∠ACE = 10°.

Calculate :  Angle BEC,

Exercise 17(A) | Q 44.2 | Page 261

In the given figure, AC is the diameter of circle, centre O. CD and BE are parallel. Angle AOB = 80o and angle ACE = 10o. Calculate : Angle BCD

Exercise 17(A) | Q 44.3 | Page 261

In the given figure, AC is the diameter of circle, centre O. CD and BE are parallel. Angle AOB = 80o and angle ACE = 10o. Calculate: Angle CED.

Exercise 17(A) | Q 45 | Page 261

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ABC+∠CDE. Give reasons for your answer.

Exercise 17(A) | Q 46 | Page 261

In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, Calculate ∠DEC .

Exercise 17(A) | Q 47 | Page 261

Use the given figure to find:
(ii) ∠DQB

Exercise 17(A) | Q 48.1 | Page 261

In the given figure, AOB is a diameter and DC is parallel to AB. If ∠CAB = x°; find (in terms of x) the values of ;
∠COB,

Exercise 17(A) | Q 48.2 | Page 261

In the given figure, AOB is a diameter and DC is parallel to AB. If  ∠ CAB = xo ; find (in terms of x) the values of: ∠ DOC.

Exercise 17(A) | Q 48.3 | Page 261

In the given figure, AOB is a diameter and DC is parallel to AB. If  ∠ CAB = xo ; find (in terms of x) the values of: ∠ DAC

Exercise 17(A) | Q 48.4 | Page 261

In the given figure, AOB is a diameter and DC is parallel to AB. If  ∠ CAB = xo ; find (in terms of x) the values of: ∠ ADC.

Exercise 17(A) | Q 49 | Page 262

In the given figure, AB is the diameter of a circle with centre O. ∠BCD = 130°. Find:
(i) ∠DAB
(ii) ∠DBA

Exercise 17(A) | Q 50 | Page 262

In the given figure, PQ is the diameter of the circle whose centre is O. Given ∠ROS = 42°, Calculate ∠RTS.

Exercise 17(A) | Q 51 | Page 262

In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that ∠PQR = 58°,
Calculate:
(i) ∠RPQ, (ii) ∠STP

Exercise 17(A) | Q 52.1 | Page 262

AB is the diameter of the circle with centre O. OD is parallel to BC and ∠AOD = 60°. Calculate the numerical values of :  ∠ABD

Exercise 17(A) | Q 52.2 | Page 262

AB is the diameter of the circle with centre O. OD is parallel to BC and  ∠ AOD = 60° ; calculate the numerical values of:  ∠ DBC

Exercise 17(A) | Q 52.3 | Page 262

AB is the diameter of the circle with centre O. OD is parallel to BC and  ∠ AOD = 60° ; calculate the numerical values of:  ∠ ADC

Exercise 17(A) | Q 53.1 | Page 262

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find :  ∠AOB

Exercise 17(A) | Q 53.2 | Page 262

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find :  ∠ACB

Exercise 17(A) | Q 53.3 | Page 262

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find :  ∠ABD

Exercise 17(A) | Q 53.4 | Page 262

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find :  ∠ADB

Exercise 17(A) | Q 54.1 | Page 262

In the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find: ∠BCD
Hence, show that AC is a diameter

Exercise 17(A) | Q 54.2 | Page 262

In the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find: ∠ ACB.

Hence, show that AC is a diameter.

Exercise 17(A) | Q 55 | Page 262

In a cyclic quadrilateral ABCD, ∠A : ∠C = 3 : 1 and ∠B : ∠D = 1: 5; Find each angle of the quadrilateral .

Exercise 17(A) | Q 56 | Page 262

The given figure shows a circle with centre O and ∠ABP = 42°

Calculate the measure of:
(i) ∠PQB
(ii) ∠QPB + ∠PBQ

Exercise 17(A) | Q 57.1 | Page 262

In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.

If ∠MAD = x and ∠BAC = y :  express ∠AMD in terms of x.

Exercise 17(A) | Q 57.2 | Page 262

In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.

If ∠MAD = x and ∠BAC = y :  express ∠ABD in terms of y.

Exercise 17(A) | Q 57.3 | Page 262

In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.

If ∠MAD = x and ∠BAC = y , Prove that : x = y

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 17 Circles Exercise 17(B) [Page 265]

Exercise 17(B) | Q 1 | Page 265

In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal. Prove it.

Exercise 17(B) | Q 2.1 | Page 265

In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate:  ∠AEF

Exercise 17(B) | Q 2.2 | Page 265

In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate:  ∠ FAB.

Exercise 17(B) | Q 3 | Page 265

If two sides of a cyclic quadrilateral are parallel; prove that:
(i) its other two sides are equal.
(ii) its diagonals are equal.

Exercise 17(B) | Q 4 | Page 265

The given figure shows a circle with centre O. Also, PQ = QR = RS and ∠PTS = 75°. Calculate:
(i) ∠POS,  (ii) ∠QOR,  (iii) ∠PQR.

Exercise 17(B) | Q 5 | Page 265

In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight sided polygon inscribed in the circle with centre O. Calculate the sizes of:
(i) ∠AOB,  (ii) ∠ACB  (iii) ∠ABC

Exercise 17(B) | Q 6 | Page 265

In a regular pentagon ABCDE, Inscribed in a circle; find ratio between angle EDA and angle ADC.

Exercise 17(B) | Q 7.1 | Page 265

In the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠AEB

Exercise 17(B) | Q 7.2 | Page 265

In the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠AED

Exercise 17(B) | Q 7.3 | Page 265

In the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠ COD.

Exercise 17(B) | Q 8.1 | Page 265

In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108°, find : ∠CAB

Exercise 17(B) | Q 8.2 | Page 265

In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108° find : ∠ ADB.

Exercise 17(B) | Q 9 | Page 265

The figure shows a circle with centre O. AB is the side of regular pentagon and AC is the side of regular hexagon.
Find the angles of triangle ABC.

Exercise 17(B) | Q 10 | Page 265

In the given figure, BD is a side of a regular hexagon, DC is a side of a regular pentagon and AD is a diameter. Calculate :

(i) ∠ADC (ii) ∠BDA, (iii) ∠ABC, (iv) ∠AEC.

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 17 Circles Exercise 17(C) [Pages 265 - 267]

Exercise 17(C) | Q 1 | Page 265

In the given circle with diameter AB, find the value of x.

Exercise 17(C) | Q 2 | Page 265

In the given figure, ABC is a triangle in which ∠BAC = 30°. Show that BC is equal to the radius of the circumcircle of the triangle ABC, whose centre is O.

Exercise 17(C) | Q 3 | Page 265

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Exercise 17(C) | Q 4 | Page 266

In the given figure, chord ED is parallel to diameter AC of the circle. Given ∠CBE = 65°, calculate ∠DEC.

Exercise 17(C) | Q 5 | Page 266

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic. Prove it.

Exercise 17(C) | Q 6.1 | Page 266

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BDC

Exercise 17(C) | Q 6.2 | Page 266

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BEC

Exercise 17(C) | Q 6.3 | Page 266

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BAC

Exercise 17(C) | Q 7 | Page 266

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

Exercise 17(C) | Q 8 | Page 266
In the given figure, ABCD is a cyclic quadrilateral. AF is drawn parallel to CB and DA is produced to point E. if ∠ADC = 92°, ∠FAE = 20°; determine ∠BCD. Give reason in support of your answer.
Exercise 17(C) | Q 9.1 | Page 266

If I is the incentre of triangle ABC and AI when produced meets the circumcircle of triangle ABC in point D. If ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠DBC

Exercise 17(C) | Q 9.2 | Page 266

If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D . if ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠IBC

Exercise 17(C) | Q 9.3 | Page 266

If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D. f ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠BIC.

Exercise 17(C) | Q 10 | Page 266

In the given figure, AB = AD = DC = PB and ∠DBC = x°. determine, in terms of x : (i) ∠ABD, (ii) ∠APB
Hence or otherwise, prove that AP is parallel to DB.

Exercise 17(C) | Q 11 | Page 266

In the given figure; ABC, AEQ and CEP are straight lines. Show that ∠APE and ∠CQE are supplementary.

Exercise 17(C) | Q 12 | Page 266

In the given figure, AB is the diameter of the circle with centre O.

If ∠ADC = 32°, find angle BOC

Exercise 17(C) | Q 13 | Page 266

In a cyclic – quadrilateral PQRS, angle PQR = 135°. Sides SP and RQ produced meet at point A : whereas sides PQ and SR produced meet at point B.
If ∠A : ∠B = 2 : 1; find angles A and B.

Exercise 17(C) | Q 14 | Page 266

In the following figure, ABCD is a cyclic quadrilateral in which AD is parallel to BC.

If the bisector of angle A meets BC at point E and the given circle at point F, Prove that:
(i) EF = FC (ii) BF = DF

Exercise 17(C) | Q 15 | Page 266

ABCD is a cyclic quadrilateral. Sides AB and DC produced meet at point E; whereas sides BC and AD produced meet at point F.   If ∠DCF : ∠F : ∠E = 3 : 5 : 4, Find the angles of the cyclic quadrilateral ABCD.

Exercise 17(C) | Q 16 | Page 267

The following figure shows a circle with PR as its diameter.
If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.

Exercise 17(C) | Q 17 | Page 267

In the following figure, AB is the diameter of a circle with centre O.
If chord AC = chord AD, Prove that:
(i) arc BC = arc DB
(ii) AB is bisector of ∠CAD.
Further, if the length of arc AC is twice the length of arc BC, find : (a) ∠BAC (b) ∠ABC

Exercise 17(C) | Q 18 | Page 267

In cyclic quadrilateral ABCD; AD = BC, ∠BAC = 30° and ∠CBD = 70°; find:
(i) ∠BCD (ii) ∠BCA (iii) ∠ABC (iv) ∠ADC

Exercise 17(C) | Q 19 | Page 267

In the given figure, ∠ACE = 43° and ∠CAF = 62° ; Find the values of a, b and c.

Exercise 17(C) | Q 20 | Page 267

In the given figure, AB is parallel to DC ∠BCE = 80° and ∠BAC = 25°.

Find:

Exercise 17(C) | Q 21 | Page 267

ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, Show that APB = 60°

Exercise 17(C) | Q 22 | Page 267

In the figure, given alongside, CP bisects angle ACB. Show that DP bisects angle ADB.

Exercise 17(C) | Q 23 | Page 267

In the figure, given below, AD = BC, ∠BAC = 30° and ∠CBD = 70°.
Find:   (i) ∠BCD (ii) ∠BCA (iii) ∠ABC (iv) ∠ADB

Exercise 17(C) | Q 24.1 | Page 267

In the figure given below, an AD is a diameter. O is the centre of the circle AD is parallel to BC and angle CBD = 32°. Find  angle OBD

Exercise 17(C) | Q 24.2 | Page 267

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.

Find: ∠AOB

Exercise 17(C) | Q 24.3 | Page 267

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.

Find: ∠BED

Exercise 17(C) | Q 25 | Page 267

In the figure given, O is the centre of the circle. angle "DAE" = 70^@, Find giving suitable reasons the measure of:

1) angle "BCD"

2) angle "BOD"

3) angle "OBD"

Chapter 17: Circles

Exercise 17(A)Exercise 17(B)Exercise 17(C)

Selina solutions for Concise Mathematics Class 10 ICSE chapter 17 - Circles

Selina solutions for Concise Mathematics Class 10 ICSE chapter 17 (Circles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 17 Circles are Tangent to a Circle, Number of Tangents from a Point on a Circle, Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord, Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof), Chord Properties - Equal Chords Are Equidistant from the Center, Chord Properties - Chords Equidistant from the Center Are Equal (Without Proof), Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line, Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle, Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof), Arc and Chord Properties - Angle in a Semi-circle is a Right Angle, Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse, Arc and Chord Properties - If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof), Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal, Cyclic Properties, Concept of Circles, Areas of Sector and Segment of a Circle, Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments, Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection, Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.

Using Selina Class 10 solutions Circles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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