Chapter 10 : Tangents to a circle

Exercise - 20

1. In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6cm, BC = 7cm and CD = 4cm. Find AD.

2. In figure. l and m are two parallel tangents at A and B. The tangent at C makes an intercept DE between the tangent l and m. Prove that .

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

4. In figure, a circle is inscribed in a having sides AB = 12 cm, BC = 8cm and AC = 10cm. Find AD, BE and CF.

5. A circle is touching the side BC of a at P and is touching AB and AC when produced at Q and R. Prove that AQ = ½ (Perimeter of )

6. In figure. Two circles intersects each other at A and B. the common chord AB is produced to meet the common tangent PQ to the circle at D. Prove that DP = DQ.

7. In figure. XP and XQ are two tangents to a circle with centre O from a point X out side the circle. ARB is a tangent to the circle at R. prove that XA + AR = XB + BR.

8. A circle touches all the four sides a quadrilateral ABCD. Prove that the angles subtended at the centre of the circle by the opposite sides are supplementary.

9. If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is the perpendicular perpendicular bisector of AB.

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