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 congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that |__PTQ = 2 |__OPQ .

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.

Let A be one point of intersection of two intersecting circles with centres O and Qd . The tangents at A to the two circles meet the circles again at B and C respectively. Let the point P be located so that AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC.

Two circles intersect each other. Then the total number of common tangents that can be drawn to them is :

Two concentric circles with centre O are of radius 3 cm and 5 cm. From an external point P, two tangents PB and PA are drawn to these circles respectively. If PA=12 cm, find PB.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

A line intersecting a circle in two points is called a secant .

A secant is a line which intersects the circle at two distinct points and the line segment between the points is a chord.