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.

Answer 1

Given: Point C is the centre of the circle.

chord PM ≅ chord PN

To prove: Ray PC is the bisector of ∠NPM.

Proof:

Draw seg CM and seg CN.

In ∆CPM and ∆CPN,

seg PM ≅ seg PN      ...(Given)

seg PC ≅ seg PC      ...(Common side)

seg CM ≅ seg CN      ...(radii of the same circle)

∴ ∆CPM ≅ ∆CPN      ...(By SSS congruency)

∴ ∠CPM ≅ ∠CPN      ...(c.a.c.t.)

∴ Ray PC is the bisector of ∠NPM.