Question

AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.

Answer 1

Given: Two circles with centre’s O and O'. AB and CD are common tangents to the circles which intersect in P.

To Prove: AB = CD

Proof:

AP = PC (length of tangents drawn from an external point to the circle are equal)                              ..… (1) 

PB = PD (length of tangents drawn from an external point to the circle are equal)                              ..… (2) 

Adding (1) and (2), we get

AP + PB = PC + PD

⇒ AB = CD
Hence Proved