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

Asked by ponmani | 3rd Mar, 2011, 12:38: PM

Expert Answer:

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

Answered by  | 3rd Mar, 2011, 08:53: AM

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