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 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 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 cirlces intersect at P and Q . Through P diameter PA and PB of the two circles are drawn. Show that the points A,Q and B are collinear.

Prove that q^^~p -=~ (q to p)

Two congruent circles intersect each other at points A and B. Through A any linesegment PAQ is drawn so that P, Q lie on the two circles. Prove that B P\ =\ B Q .

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 .

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 .

P Q and R S are two parallel chords of a circle and lines R P and S Q intersect each other at O as shown in Figure. Prove that O P=O Qdot

In triangle ABC, P is the mid-point of side BC. A line through P and parallel to CA meets AB at point Q and a line through Q and a line through Q and parallel to BC meets median AP at point R. Prove that : BC=4QR .