If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

Two intersecting circles have a common tangent or not?

A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle,Prove that R bisects the arc PRQ.

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that square ABCD is cyclic.

Number of tangents drawn from a point inside the circle is :

Theorem: The length of two tangents drawn from an external point to a circle are equal.

PA and PB are the two tangents drawn on a circle from and external point P. The centre of the circle is O and the tangents touches the circles at points A and B. Then quadrilateral OAPB is-

Perpendiculars are drawn,respectively,from the points P and Q to the chords of contact of the points Q and P with respect to a circle. Prove that the ratio of the length of perpendiculars is equal to the ratio of the distances of the points P and Q from the center of the circles.

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