Q. 34.0( 40 Votes )

Seg PM and seg PN are congruent chords of a circle with center C. Show that the ray PC is the bisector of NPM.

Answer :


Given that PM = PN


We know that Congruent chords of a circle are equidistant from the center of the circle.


Therefore, AC = CB ………………(1)


Also,


A perpendicular drawn from the centre of a circle on its chord bisects


the chord.


CB bisects PN as PB = BN,


Similarly, CA bisects PM as PA = AM.


In ΔAPC and ΔBPC,


CAP = CBP = 90°


PC = PC (common side)


AC = CB (From eq (1))


ΔAPC ΔBPC (RHS congruence)


APC = BPC (by CPCT)


Hence proved that PC is the bisector of NPM.


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