Question

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove they are equal.
Please explain with diagram.

Answer 1

Answer:

Step-by-step explanation:

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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

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