Question

In the given figure, $△ABC$ is an isosceles triangle with $AB=AC$ and $O$ is the centre of the circle. If $\angle AOB=\alpha$ and $\angle AOC=\beta$, then which of the following is true?

• A. $\alpha =2\beta$
• B. $\alpha =\frac{\beta }{2}$
• C. $\alpha =\beta$
• D. $\alpha =3\beta$

Answer 1

The correct option is C

$\alpha =\beta$

$AB$ and $AC$ are equal chords of the circle.

Angle subtended by chord $AB$ at the centre =$\angle AOB=\alpha$

Angle subtended by chord $AC$ at the centre= $\angle AOC=\beta$.

We know that equal chords subtend equal angles at the centre.

$\Rightarrow \angle AOB=\angle AOC$

i.e., $\alpha =\beta$