CBSE: 10th Class Sample Test Paper - 2011

Tangent to Circle

Q.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.

Q.2. Tangent to a circle is a line which intersects the circle in exactly one point.

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 ﮮDEF = 90 .

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

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

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

Q.6. In figure. Two circles intersect 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.

Q.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.

Q.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.

Q.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 bisector of AB.

Q.10. If PAB is a secant to a circle intersecting it at A and B and PT is a tangent Then PA.PB = PT².