Question

In the given figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisectors of ∠BAC.

Answer 1

Given: AB and AC are two equal chords of a circle with centre O.
To prove: ∠OAB = ∠OAC

Proof:
In ΔOAB and ΔOAC, we have:
AB = AC (Given)
OA = OA (Common)
OB = OC (Radii of a circle)
∴ ΔOAB ≅ ΔOAC (By SSS congruency rule)
i.e.,∠OAB = ∠OAC (CPCT)
Hence, point O lies on the bisector of ∠BAC.