In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

Question

Philoid · Accepted Answer

We have to prove AB = CD.

Let P be the point of intersection of AB and CD.

We know that the length of two tangents drawn from an external point to a circle is equal.

∴ AP = CP … (1)

BP = DP … (2)

Adding (1) and (2), we get

⇒ AP + BP = CP + DP

⇒ AB = CD

Ans. Hence proved that AB = CD.