Two circles intersects in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that the A,Q,B and T lie on a circle.

Two equal circles intersect in P and Q . A straight line through P meets the circles in A and B . Prove that Q A=Q Bdot

Two equal circles intersect in P and Q . A straight line through P meets the circles in A and B . Prove that Q A=Q Bdot

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

Two circles C_1 and C_2 intersect at two distinct points P and Q in a line passing through P meets circles C_1 and C_2 at A and B , respectively. Let Y be the midpoint of A B and Q Y meets circles C_1 and C_2 at X a n d Z respectively. Then prove that Y is the midpoint of X Z

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Figure). Prove that /_A C P=/_Q C D .

In the figure, PO_|_QO. The tangents to the circle with centre O at P and Q intersect at a point T. Prove that PQ and OT are right bisectors of each other.

Two circle intersect in A and B and AC and AD are respectively the diameters of the circles. Prove that C , B , D are collinear.

In the adjoining figure, common tangents AB and CD to two circles intersect at P. Prove that AB=CD.

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that /_A C P\ =/_Q C D .

In Figure, common tangents P Qa n dR s to two circle intersect at Adot Prove that P Q=R Sdot