Question

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

Answer 1

Hey!!! Mate here is your answer :

Let the two circles intersect at points X and Y. XY is the common chord.

Suppose A is a point on the common chord and AM and AN be the tangents drawn from A to the circle.

AM is the tangent and AXY is a secant.

∴ AM2 = AX × AY …....(1)

AN is the tangent and AXY is a secant.

∴ AN2 = AX × AY …..........(2)

From (1) and (2), we get

AM2 = AN2

∴ AM = AN