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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
▶ 14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
19: Trigonometry
20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 14 - Circles (Chord and Arc Properties) - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 14 - Circles (Chord and Arc Properties)")
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Solutions for Chapter 14: Circles (Chord and Arc Properties)
Below listed, you can find solutions for Chapter 14 of CISCE B Nirmala Shastry for Mathematics [English] Class 9 ICSE.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 14 Circles (Chord and Arc Properties) EXERCISE 14A [Pages 173 - 174]
The diameter of a circle is 50 cm. A chord is at a distance of 7 cm from the centre of the circle. Find the length of the chord.
The length of a chord is 30 cm and it is at a distance of 8 cm from the centre of the circle. Find the radius.
The diameter of a circle is 82 cm and the length of a chord is 80 cm. Calculate the distance of the chord from the centre of the circle.
Two parallel chords in a circle are 10 cm and 24 cm long. If the radius of the circle is 13 cm, find the distance between the chords if they lie:
- on the same side of the centre
- on the opposite sides of the centre.
Two parallel chords of a circle are on the opposite sides of the centre of a circle of radius 25 cm. If one chord is 48 cm long, find the length of the other chord if the distance between the chords is 27 cm.
Two parallel chords in a circle are at a distance of 44 cm from each other. If they lie on the opposite sides of the centre and are respectively 80 cm and 96 cm long, calculate the radius of the circle.
The radii of two concentric circles are 15 cm and 20 cm. A line segment ABCD cuts the outer circle at A and D and inner circle at B and C. If BC = 18 cm, find the length of AB.
An isosceles triangle ABC is inscribed in a circle when AB = AC = 20 cm and BC = 24 cm. Find the radius of the circle.
PQR is an isosceles triangle inscribed in a circle. Calculate the radius of the circle if PQ = PR = 50 cm and QR = 60 cm.
An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.
AB is the diameter of a circle. P is a point on it such that AP = 24 cm and PB = 6 cm. Find the length of the shortest chord through P.
The length of the common chord AB of two intersecting circles is 18 cm. If the diameters of the circles are 82 cm and 30 cm, calculate the distance between the centres.
In the given circle with centre O, AD = DB = 16 cm and DE = 8 cm. Find the radius of the circle.
In the given figure, AD is the chord of the larger of the two concentric circles and BC is the chord of the smaller circle. Prove that AB = CD.
Triangle ABC is inscribed in a circle with centre O, AB = AC, OP ⊥ AB and OQ ⊥ AC. Prove that PB = QC.
ABCD is a square, C is the centre of the circle. Prove that AP = AR.
In the figure, given below, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of lengths 24 cm and 18 cm respectively.
In the given figure, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the:
- radius of the circle.
- length of chord CD.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 14 Circles (Chord and Arc Properties) EXERCISE 14B [Pages 177 - 178]
In the given circle, O is the centre. Chords AD = CD, If ∠ABC = 40°, find ∠ABD, ∠BOC and ∠COD.
In the quadrilateral ABCD, AB = CD and ∠CAD = 35°. Find ∠ACB and prove that ABCD is an isosceles trapezium.
In the circle with centre O, PQ = QR = RS and ∠QOS = 116°. Calculate ∠POQ, ∠OQR, ∠OQS and ∠SQR.
In the circle with centre O, ∠BOD = 160° and chord BC = chord CD. Find ∠BOC, ∠OBD, ∠OBC and ∠CBD.
AB is a side of a regular hexagon and BC is a side of a regular nonagon. Find ∠BOC, ∠AOB, ∠OBC, ∠OAC and ∠ABC.
In the given figure, A, B, C are 3 points on the circumference of a circle with centre O. Arc AB = 2 arc BC and ∠AOB = 108°.
Calculate:
- ∠BOC
- ∠OAB
- ∠OAC
- ∠BAC
In the circle, O is the centre, chords AE = AD = DC and ∠ABC = 56°. Find ∠CBD, ∠CBE, ∠BOC and ∠COD.
In the semicircle with centre O, chords PQ = QR = RS. Find ∠QOR, ∠OPR, ∠OPQ and ∠QPR.
In the semi-circle with centre O, PO ⊥ diameter AB. ∠ACB = 90°, AC = 24 cm and CQ = 7 cm. Find the length of BQ, AB and PQ.
O is the centre of a circle. If PS = QR, ∠PQS = 24°, find ∠QPR, ∠OSQ and ∠POS.
In the circle with centre O, BO ⊥ diameter AD. Chord BC = chord DE. Find the angles p, q, r and ∠AOE.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 14 Circles (Chord and Arc Properties) MULTIPLE CHOICE QUESTIONS [Pages 178 - 179]
The line segment joining any 2 points on a circle is called a ______.
radius
chord
tangent
secant
The longest chord of the circle is ______.
radius
tangent
diameter
segment
The diameter of a circle is 100 cm. The length of a chord is 60 cm. The distance of the chord from the centre is ______.
80 cm
60 cm
50 cm
40 cm
The length of a chord is 40 cm. It is 15 cm from the centre. The radius of the circle is ______.
50 cm
41 cm
25 cm
30 cm
AB = 16 cm, OM = 15 cm, ON = 8 cm
radius =
20 cm
25 cm
17 cm
30 cm
AB = 16 cm, OM = 15 cm, ON = 8 cm
CD =
15 cm
30 cm
13 cm
26 cm
3(Arc BC) = Arc AB, ∠AOB = 120°, ∠BOC =
60°
50°
45°
40°
AM = MB, ∠AOB = 140°
∠OAB =
40°
30°
20°
35°
AM = MB, ∠AOB = 140°
∠AOM =
70°
60°
50°
40°
AM = MB, ∠AOB = 140°
∠OAM =
50°
55°
60°
45°
O and C are centres of the two circles. The 2 radii are 15 cm and 13 cm. If AB = 24 cm. The length of OC is ______.
10 cm
17 cm
15 cm
14 cm
O is the centre of the circle. CD is a side of a regular octagon. ∠COD = 45°, AB is a side of a regular pentagon. Find ∠AOB.
60°
80°
72°
40°
In each of the following questions, a statement of assertion (A) is given and a statement of Reason (R) given below it choose the correct option for each question.
Assertion: Congruent circles are concentric.
Reason: Concentric circles have same centre with different radii.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: ABCDE is a regular pentagon inscribed in a circle with centre O. ∠OCE = 18°.
Reason: Equal chords make equal angles at the centre.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: Through 3 non collinear points A, B, C many circles can be drawn.
Reason: The 2 perpendicular bisectors of AB and BC meet at one point which is the centre of the circle.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: Two circles can intersect at 3 points.
Reason: Two circles can intersect at 2 points.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion: In the circle with centre O, AB = 18 cm, OA = 15 cm and ON ⊥ AB. ∴ MN = 3 cm
Reason: Perpendicular from the centre to a chord bisects the chord.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE 14 Circles (Chord and Arc Properties) MISCELLANEOUS EXERCISE [Pages 179 - 180]
The diameter of a circle is 26 cm. A chord of the circle is at a distance of 5 cm from the centre of the circle. Find the length of the chord.
O is the centre of the circle. OM ⊥ chord AB and ON ⊥ chord CD. AB = 40 cm, OM = 15 cm, ON = 7 cm.
Find the
- radius of the circle,
- length of the chord CD.
In the given circle with centre O, AM = MB = 12 cm and MC = 6 cm. Find the radius of the circle.
The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts outer circle at P and S and inner circle at Q and R. If QR = 12 cm, find the length of PQ.
An isosceles triangle ABC is inscribed in a circle when AB = AC = 10 cm and BC = 12 cm. Find the radius of the circle.
Two circles with centres O and P intersect at A and B. AB = 24 cm and the diameters are 30 cm and 26 cm. Calculate the length of OP.
ABCO is a quadrilateral inscribed in the circle with centre O, Chord AB = Chord BC and ∠AOC = 136°. Calculate:
- ∠AOB
- ∠OAC
- ∠OAB
- ∠BAC
Chord PS = chord SR = chord PT in the circle with centre O and ∠PQR = 50°. Calculate:
- ∠PQS
- ∠TQR
- ∠QOR
- ∠POR
- ∠POS
O is the centre of the circle in which arc AB = 2 × arc BC. If ∠AOB = 104°, find
- ∠BOC
- ∠OAB
- ∠OCA
- ∠OBC
In the given circle with centre O, AB = BC = CD and ∠AOB = 40°. Calculate:
- ∠AOD
- ∠OAD
- ∠BOD
- ∠OBD
O is the centre of the circle. Arc AB = Arc BC = Arc CD. If ∠OAB = 48°, find
- ∠AOB
- ∠BOD
- ∠OBD
AB is the diameter of the circle with centre O. OM ⊥ AD and ON ⊥ BC, OM = ON. ∠AOD = 70°. Find:
- ∠BOC
- ∠DOC
- ∠ODB
Solutions for 14: Circles (Chord and Arc Properties)
B Nirmala Shastry solutions for Mathematics [English] Class 9 ICSE chapter 14 - Circles (Chord and Arc Properties)
Shaalaa.com has the CISCE Mathematics Mathematics [English] Class 9 ICSE CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. B Nirmala Shastry solutions for Mathematics Mathematics [English] Class 9 ICSE CISCE 14 (Circles (Chord and Arc Properties)) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Mathematics [English] Class 9 ICSE chapter 14 Circles (Chord and Arc Properties) are Basic Concept of Circle, Chord, Theorems on Angles in a Circle, Arc of the Circle, Segment of a Circle, Sector of a Circle.
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