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

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#### 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 = CDHence Proved*

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