Two circles intersect at A and B. From a point P on one of the circles lines PAC and PBD are drawn intersecting the second circle at C and D. Prove that CD is parallel to the tangent at P.

Two circle intersect at two points B and C. Through B, Two lines segment ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ACP = QCD .

Two cocentric circle common centre O. A line 'l' intersects these circle A,B,C and D. Prove that AB = CD.

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

Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is

Two circles whose centres are O and O' intersect at P. Through P, a line l parallel to OO' intersecting the circles at C and D is drawn.Prove that CD=2OO

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 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 given figure, two circles with centres O and O' touch externally at a point A. A line through A is drawn to intersect these circles at B and C. Prove that the tangents at B and C are parallel.

Point O is the centre of a circle . Line a and line b are parallel tangents to the circle at P and Q. Prove that segment PQ is a diameter of the circle.