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 circle intersect at a point X and Y , XY is the common chord.
Suppose A is a point on their common chord and AM and AN be the tangent drawn from A to the circle
AM is the tangent and AXY is a secant.
AM2 = AX×AY ............(i)
AN is the tangent and AXY is the secant.
AN2 = AX×AY ............(i)
Therefore, from equations (i) and (ii), we get,
AM = AN.