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 $AP + PB = CP + PD \Rightarrow AB = CD$ $\\$ MathematicsConcise MathematicsStandard X

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