Answer the following
1. In the below Figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.
2. A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal.
3. In the below figure, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.
4. In the below figure, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠ RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠ RQS.
5. In the below figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.
6. Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
7. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that APB = 2<OAB
8. In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.
9. In the below figure, two equal circles, with centres O and O', touch each other at X.OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular to AC. Find the value of DO'/CO.
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