if from any point on the common chord of two intersecting circles,tangents be drawn to the circles,prove that they are equal.
Let the two circles intersect at points M and M. MN is the common chord.
Suppose O is a point on the common chord and OP and OQ be the tangents drawn from A to the circle.
OP is the tangent and OMN is a secant.
According to the theorem which says that if PT is a tangent to the circle from an external point P and a secant to the circle through P intersects the circle at points A and B, then PT2 = PA × PB