Question

In the figure, common tangents AB and CD to the two circles intersect at E. Prove that AB =CD.

Answer 1

Given : Two non-intersecting circles are shown in the figure. Two intersecting tangents AB and CD intersect at E. E point is between the circles and outside also.

To prove : $AB=CD$

Proof : We know that tangents drawn from an external point (E) to a circle are equal. Point E is outside of both the circles.

So, $EA=EC$ ___(i)

$EB=ED$ ___(ii)

$\Rightarrow EA+EB=EC+ED$ [Adding (i) and (ii)]

$\Rightarrow AB=CD$

Hence, proved.