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

Posted by Gupta Shivaay 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 10 months ago

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

2Thank You

ANSWER

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