#### Question

In Figure 1, common tangents AB and CD to the two circles with centres 0_{1}and 0_{2 }intersect at E. Prove that AB = CD.

#### Solution

Given: AB and CD are common tangents to both the circles.

To prove: AB = CD

Proof:

We know that two tangents drawn to a circle for the same exterior point are

equal.

Thus we get

AE = EC (i)

Similarly

ED = EB (ii)

AB = AE + EB (iii)

and

CD = CE + ED (iv)

AB = EC + EB from (i) and (iii)

CD = EC + EB from (ii) and (iv)

Therefore AB = CD

Hence proved.

Is there an error in this question or solution?

Solution common tangents AB and CD to the two circles with centres 01and 02 intersect at E. Prove that AB = CD. Concept: Circles Examples and Solutions.