Question

An equilateral $\Delta ABC$ is inscribed in a circle with centre O. The measure of $\angle BOC$ is :

• A. ${110}^{\circ }$
• B. ${100}^{\circ }$
• C. ${120}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is C ${120}^{\circ }$

$△ABC$ is an equilateral triangle inscribe in circle with center $O.$

$\therefore$ $\angle ABC=\angle BCA=\angle BAC={60}^o$ [ Angles of an equilateral triangle ]

$\Rightarrow$ Chord $BC$ subtends $\angle BOC$ at the center and $\angle BAC$ on the circle.

Angle subtended at the center of circle is double at any point on circumference of circle.

$\therefore$ $\angle BOC=2\angle BAC$

$\Rightarrow$ $\angle BOC=2\times {60}^o$

$\therefore$ $\angle BOC={120}^o.$