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 $∠$ BAC.

Open in App

Solution

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.

Suggest Corrections

Similar questions

Q. 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.

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 $∠$ BAC.

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.

Show that the bisector of angle BAC is a perpendicular bisector of chord BC

A B

and

A C

are two equal chords of a circle. Prove that the bisector of the

∠ B A C

passes through the centre of the circle.

Two circle with centres O and O' are drawn to intersect each other at points A and B.

Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects $∠ B A C$

Join BYJU'S Learning Program

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 ∠BAC.

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 $∠$ BAC.