Question

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $\angle$BAC.

Answer 1

Given: AB and AC are two equal chords of a circle with centre O.
To prove: ∠ OAB = ∠ OAC
Construction: Join OA, OB and OC.
Proof:
In Δ OAB and Δ OAC, we have:
AB = AC
(Given)
OA = OA
(Common)
OB = OC
(Radii of a circle)
∴ Δ OAB ≅ Δ OAC (By SSS congruency rule)
⇒ ∠ OAB = ∠ OAC (CPCT)
Hence, point O lies on the bisector of ∠ BAC.