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Question

Chords AB and CD of a circle intersect each other at point P such that AP = CP.

Show that : AB = CD.


Solution

Given AB  and CD  intersect at P

AP = CP  (given)

Therefore AP \times PB = CP \times PD

\Rightarrow \frac{AP}{CP} = \frac{PD}{PB}

\Rightarrow PD = PB

Therefore AP + PB = CP + PD \Rightarrow AB = CD 

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Mathematics
Concise Mathematics
Standard X

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