Question

If from any point on the common chord of two intetsecting circles two tangents are drawn on them ,prove that they are equal

Answer 1

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here is your answer
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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