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

Dear Student,

Tangents cant be drawn from the common chord unless we produce it .The reason to it is if we try to draw tangent from any point except the 2 intersecting points then it will pass the circles from 2 points. and if we try to draw from the point of intersection then the common chord itself intersects the circles and we can't draw tangents from to a circle from any point on the circle itself and if we produce the chord and then draw 2 tangents then ,

if we consider the common chord as AB. the ext point as P and the tangents as PM and PN. then

PM=PA ,                      [tangents from an ext point are equal in length]   ...............1

PN=PA,                       [tangents from an ext point are equal in length]   ...............2

thus, from 1 and 2

PM=PN

hence proved.

 

Regards

Team Topperlearning