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Question

AB and CD are the chords of a circle whose center is O. They intersect each other at P. If PO is the bisector of APD, prove that AB = CD. [2 MARKS]


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Solution

Concept: 1 Mark
Application: 1 Mark

Given :AB and CD are the chords of a circle whose center is O.
They intersect each other at P.
PO is the bisector of APD


To prove: AB = CD

Construction: Draw ORAB and OQCD.

Proof: In ΔOPR and ΔOPQ

OPR=OPQ (Given)

OP=OP (Common)

ORP=OQP (Each =90 by construction)

ΔOPR=ΔOPQ (AAS congruency)

OR=OQ (C.P.C.T)

AB=CD ( chord of a circle which are equidistant from the center are equal).


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