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