# Ncert Solutions For Class 10 Maths Chapter 10 Circles

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## In this pdf file you can see answers of following Questions

### EXERCISE 10.1

Question 1. How many tangents can a circle have? 2. Fill in the blanks :
(i) A tangent to a circle intersects it in point (s).
(ii) A line intersecting a circle in two points is called a .
(iii) A circle can have parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called .

Question 2. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) 119 cm.

Question 3. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

### EXERCISE 10.2

Question 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

Question 2. In Fig. 10.11, 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°

Question 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°

Question 4. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Question 5. 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.

Question 6. 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.

Question 7. A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC Fig. 10.12 Fig. 10.13

Question 8. In Fig. 10.13, 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°.

Question 9. 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.

Question 10. Prove that the parallelogram circumscribing a circle is a rhombus.

Question 11. 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 (see Fig. 10.14). Find the sides AB and AC.

Question 12. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

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