X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank for CBSE EXAMS
( 1 Mark Questions )

1. If radii of the two concentric circles are 15cm and 17cm , then find the length of each chord of one circle which is tangent to one other. Ans. 16cm

2. If two tangents making an angle of 120

^{0 } with each other , are drawn to a circle of radius 6cm, then find the angle between the two radii, which are drawn to the tangents. Ans. 60

0
3. PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that

< QPT = 60

then find <PRQ. Ans. 120

0
4. If a tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q such that OQ = 12 cm then find the length of PQ. Ans.

√119cm

5. From a point P, two tangents PA and PB are drawn to a circle C(O,r) . If OP =2r ,then what is the type of

APB. Ans. Equilateral triangle

6. If the angle between two radii of a circle is 130

,then find the angle between the tangents at the end of the radii. Ans. 50

0.

7. ABCD is a quadrilateral. A circle centred at O is inscribed in the quadrilateral. If AB = 7cm , BC = 4cm , CD = 5cm then find DA. ' Ans. 8 cm

8. In a triangle

ABC , AB = 8cm , <ABC = 90

. Then find the radius of the circle inscribed in the triangle. Ans. 2cm

( 2 Mark Questions )

9. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that OAPB is a cyclic quadrilateral.

10. If PA and PB are two tangents drawn to a circle with centre O , from an external point P such that PA=5cm and < APB = 60

, then find the length of the chord AB. Ans. 5cm

11. CP and CQ are tangents from an external point C
to a circle with centre O .AB is another tangent which touches the circle at R
and intersects PC and QC at A and B respectively . If CP = 11cm and BR = 4cm,
then find the length of BC. Ans.
7cm

12. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

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

( Three Marks Questions)

14. If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB+CD=AD+BC.

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

16. AB is a chord of length 9.6cm of a circle with centre O and radius 6cm. If the tangents at A and B intersect at point P then find the length PA. Ans. 8cm

17. The incircle of a ∆ABC touches the sides BC, CA &AB at D,E and F respectively. If AB=AC, prove that BD=CD.

18. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle

19. PQ and PR are two tangents drawn to a circle with centre O from an external point P. Prove that < QPR = 2< OQR.

( Four Marks Questions)

20. Prove that the length of tangents drawn from an external point to a circle is equal. Hence, find BC, if a circle is inscribed in a

ABC touching AB,BC &CA at P,Q &R respectively, having AB=10cm, AR=7cm &RC=5cm. Ans. 8cm

21. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following: If O is the centre of two concentric circles, AB is a chord of the larger circle touching the smaller circle at C, then prove that AC=BC.

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