In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true Class 9

In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true Class 9

Question 1.

In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true: "The centre of the circle lies on the angle bisector of ∠BAC". Class 9

Solution:

Given: O is the centre of the circle AB = AC

To Show: O lies on the angle bisector of ∠BAC

Proof:

In ∆OAB and ∆OAC

AB = AC ... [Given]

OA = OA ... [common side]

OB = OC ... [radii of the same circle]

∴ ∆OAB = ∆OAC ... [by SSS congruence]

∴ ∠BAO = ∠CAO

... [Corresponding parts of congruent triangles]

∴ OA bisects ∠BAC

∴ The centre of the circle O lies on the angle bisector of ∠BAC