An equilateral triangle ABC is inscribed in a circle with centre O. Then, ∠BOC

Question

An equilateral triangle ABC is inscribed in a circle with centre O. Then, $∠ B O C$ is equal to ___.

Options:

A . 30

^{\circ}

B . 60

^{\circ}

C . 90

^{\circ}

D . 120

^{\circ}

Answer: Option D
:
D

Given that $Δ A B C$ is equilateral.
$⟹ ∠ B A C = 60^{\circ}$
Since the angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle, we have
$∠ B O C = 2 ∠ B A C = 2 \times 60^{\circ} = 120^{\circ} .$

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