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#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Liner Equation in Two Variable

Chapter 4: Quadatric Euation

Chapter 5: Arithematic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trignometry & its Equation

Chapter 9: Circles

Chapter 10: Construction

Chapter 11: Area Related To Circles

Chapter 12: Surface Areas and Volumes

Chapter 13: Statistics and Probability

## Chapter 9: Circles

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 9 Circles Exercise 9.1 [Pages 102 - 104]

#### Choose the correct alternative:

If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is ______.

3 cm

6 cm

9 cm

1 cm

In figure, if ∠AOB = 125°, then ∠COD is equal to ______.

62.5°

45°

35°

55°

If figure AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at point A, the ∠BAT is equal to ______

65°

60°

50°

40°

From a point P which is at a distance of 13 cm from the point O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ______

60 cm

^{2}65 cm

^{2}30 cm

^{2}32.5 cm

^{2}

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance of 8 cm from A is ______

4 cm

5 cm

6 cm

8 cm

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to ______

4 cm

2 cm

`2sqrt3` cm

`4sqrt3` cm

In the following figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to ______

100°

80°

90°

75°

In figure, if PA and PB are tangents to the circle with centre 0 such that ∠APB = 50°, then ∠AOB is equal to ______

25°

30°

40°

50°

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm the length of each tangent is equal to ______

`3/2 sqrt(3)` cm

6 cm

3 cm

`3sqrt(3)` cm

In figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to ______

20°

40°

35°

45°

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 9 Circles Exercise 9.2 [Pages 104 - 106]

#### State whether the following statement is True or False:

If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.

True

False

The length of tangent from an external point on a circle is always greater than the radius of the circle.

True

False

The length of tangent from an external point P on a circle with centre O is always less than OP.

True

False

The angle between two tangents to a circle may be 0°.

True

False

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = `asqrt(2)`

True

False

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = `asqrt(3)`

True

False

The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.

True

False

If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

True

False

If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

True

False

AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = BD.

True

False

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 9 Circles Exercise 9.3 [Pages 107 - 108]

Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.

Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines .

In the figure, AB and CD are common tangents to two circles of unequal radi. Prove that AB = CD

In Question 5 above, if radii of the two circles are equal, prove that AB = CD.

In figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 9 Circles Exercise 9.4 [Pages 110 - 112]

If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.

Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the the perimeter of the triangle PCD.

If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that ∠BAT = ∠ACB

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.

In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.

AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC = 30°. The tangent at C intersects extended AB at a point D. Prove that BC = BD.

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

In figure the common tangent, AB and CD to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.

In figure. O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA = 110°, find ∠CBA see figure

If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, find the area of the triangle

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

## Chapter 9: Circles

## NCERT solutions for Mathematics Exemplar Class 10 chapter 9 - Circles

NCERT solutions for Mathematics Exemplar Class 10 chapter 9 (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 CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 10 chapter 9 Circles are Tangent to a Circle, Number of Tangents from a Point on a Circle, Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles, Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles.

Using NCERT 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 NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

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