NCERT Solution For Class 10, Maths, Chapter 10, Circles, Exercise 10.2

NCERT Solution For Class 10, Maths, Chapter 10, Circles, Exercise 10.2 consist of total thirteen questions which are mainly focused on tangent drawn at different locations in circle. Class 10, Maths, Chapter 10, Circles exercise 10.2 is given below.

Table of Contents

Class 10, Maths, Chapter 10, Exercise 10.2 Solutions

Q.1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(A) 7 cm

(B) 12 cm

(C) 15 cm

(D) 24.5 cm

Ans: Correct answer: (A)

Q.2. In Figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to

(A) 60°

(B) 70°

(C) 80°

(D) 90°

Ans: Correct answer: (B)

Q.3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to

(A) 50°

(B) 60°

(C) 70°

(D) 80°

Ans: Correct option: (A)

Q.4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

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Q.5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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Q.6. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

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Q.7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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Q.8. A quadrilateral ABCD is drawn to circumscribe a circle (see Figure). Prove that AB + CD = AD +BC

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Given: ABCD is quadrilateral and AB, BC, CD and AD are tangents.

To prove: AB + CD = AD +BC

Proof: Since lengths of two tangents drawn from an same external point of circle are equal,

∴ AP = AS

BP = BQ

DR = DS

CR = CQ

Adding these all, we get

⇒ AP + BP + DR + CR = AS + BQ + DS + CQ

⇒ (AP + BP) + (CR + DR) = (BQ + QC) + (DS + AS)

⇒ AB + CD = BC + DA (proved)

Q.9. In Figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠ AOB = 90°.

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Q.10. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

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Q.11. Prove that the parallelogram circumscribing a circle is a rhombus.

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Q.12. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

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