Question

An equilateral $△ABC$ is inscribed in a circle with centre O Then the measure of $\angle BOC$ is

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

Answer 1

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

$\Rightarrow$ $△ABC$ is an equilateral triangle inscribed in a circle with center $O$.

$\Rightarrow$ $\angle ABC=\angle BCA=\angle CAB={60}^o$ [ Angles of equilateral triangle ]

$\Rightarrow$ We know that, angle subtended at the center of a circle is double angle at any point on circumference of circle.

$\therefore$ $\angle BOC=2\angle CAB$

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

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