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In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B and ∠ C$ intersect each other at O. Join A to O. Which of the following angles does the line AO bisects?

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∠ B

∠ C

∠ B and ∠ C

∠ A

answer is D.

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Detailed Solution

Given that,
ABC is an isosceles triangle where AC=AB & bisectors of

∠ B and ∠ C

intersect at O.
Question Image

Here, OB and OC bisect ∠B and ∠C intersect at O.
Therefore,
Question Image

By the property of an isosceles triangle, we have,

Multiply both the sides with

12

, we get,

We know that the sides opposite to equal angles are equal.

∴ O B = O C (4)

Thus, by SAS congruence rule:

We know that corresponding parts of congruent triangles are equal.

Thus, AO bisects angle A.
Hence, option (4) is correct.

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