Question

if from any point on the chord of two intersecting circles tangents can be dawn to the circles prove that they are equal

Answer 1

hey

Consider 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)  [ From the theorem]

AN is the tangent and AXY is a secant.

∴ AN2 = AX × AY ..................(2)  [ From the theorem]

From (1) and (2), we get

AM2 = AN2

∴ AM = AN