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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.

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Solution

When two chords intersect inside the circle, then,

AP×PB=PD×PC

APCP=PDPB

But AP=CP ...(i)

1=PDPB

PD=PB ...(ii)

Adding (i) and (ii), we get,

AP+PD=CP+PB

AB=CD


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