In Figure 1, common tangents AB and CD to the two circles with centres O₁ and O₂ intersect at E. Prove that AB = CD.

Question

In Figure 1, common tangents AB and CD to the two circles with centres O 1 and O 2 intersect at E. Prove that AB = CD.

Philoid · Accepted Answer

From the given figure,

AE = CE and BE = ED [Since tangents drawn from an external point are equal]

On adding, we get

⇒ AE + BE = CE + ED

⇒ AB = CD

Hence proved.

In Figure 1, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB = CD.