Question

plz.... answer fast ...........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

Consider PT be 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 .

This property is used to solve the given question.

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