CBSE Class 10 Answered

Given: AB and CD are the common tangents intersecting at E.

To prove: AB = CD

Proof: Consider E as an external point and tangent DE and AE are drawn.

Then, DE = AE    ..................(1)    [Since tangents from an external point are equal]

Now for the other circle CE and BE are the two tangents drawn from point E

Then CE = BC     ................(2)     [Since tangents from an external point are equal]

Adding (1) and (2), we get

DE + CE = AE + BC

So, CD = AB