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State true or false.
In an isosceles triangle ABC, with $AB = AC$ , the bisectors of $∠ B$ and $∠ C$ intersect each other at O. Join A to O Then $OB = OC$

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True

False

answer is A.

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Detailed Solution

Given triangle is ABC.
Here,
AB=AC (as triangle is isosceles) Question Image

As, we know that the sides are equal when the angles opposite are equal.
So,

∠ B = ∠ C

Divide both sides by 2

\frac{1}{2} ∠ B = \frac{1}{2} ∠ C

\Rightarrow ∠ OBC = ∠ OCB

(Angle bisectors)
And

∠ OBA = ∠ OCA

\Rightarrow OB = OC

So, side opposite equal angles is same.
So given statement is true.
Option 1 is correct.

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