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

2. From an external point P , tangents PA and PB are drawn to a circle with center O. If CD is the tangent to the circle at a point E and PA = 14 cm , find the perimeter of triangle PCD.

3. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center of the circle.

4. Two circles touch each other externally at C and AB is a common tangent to the circles. Prove that angle ACB = 90 degrees.

5. AB and CD are two common tangent to circles which touch each other at C. If D lies on AB such that CD = 4cm , then show that AB = 8cm.