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Theorem of Equal Chords Subtending Angles at the Center

Seg PM and se...

Question

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

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Solution

Join CN and CM.
In $△$ CPN and $△$ CPM,
PM $≅$ PN (Given)
PC = PC (Common)
CN = CM (Radii)
Thus, $△$ CPN $≅$ $△$ CPM (By SSS congurency)
So, $∠$ CPN = $∠$ CPM (CPCT)
Thus, ray PC is the bisector of $∠$ NPM.

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