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


 


Let the two circle intersect at a point X and Y , XY is the common chord.


 


Suppose A is a point on their common chord and AM and AN be the tangent drawn from A to the circle


 


AM is the tangent and AXY is a secant.


AM= AX×AY        ............(i)


AN is the tangent and AXY is the secant. 


AN= AX×AY        ............(i)


Therefore, from equations (i) and (ii), we get,


AM = AN.


 


 

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