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 is true?

OB = OC

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OA = OC

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AB = OB

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AC = OC

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Solution

The correct option is A OB = OC

It is given that $A B = A C$ .
$∴ ∠ B = ∠ C$
(Angles opposite to equal sides of a triangle are equal)
$\Rightarrow \frac{1}{2} (∠ B) = \frac{1}{2} (∠ C)$
OB and OC are bisectors of $∠ B$ and $∠ C$ .
$\Rightarrow ∠ O B C = ∠ O C B$
$∴$ OB = OC
(Sides opposite to equal angles are equal)

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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 is true?

The correct option is A OB = OC It is given that AB=AC. ∴∠B=∠C (Angles opposite to equal sides of a triangle are equal) ⇒12(∠B)=12(∠C) OB and OC are bisectors of ∠B and ∠C. ⇒∠ OBC=∠ OCB ∴ OB = OC (Sides opposite to equal angles are equal)

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 is true?