Q4 of 93 Page 10

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.


AM2 = AX×AY        ............(i)


AN is the tangent and AXY is the secant. 


AN2 = AX×AY        ............(i)


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


AM = AN.


 


 

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