Question

An equilateral triangle ABC, whose side is 6 cm is inscribed in a circle. Find the radius of the circle.

• A. $2$
• B. $2\sqrt{3}$
• C. $3$
• D. $3\sqrt{2}$

Answer 1

The correct option is B $2\sqrt{3}$

Given : ABC is equilateral triangle.

$OC=$ radius of cicle. $\angle ACP={60}^{\circ }$

$BC=6cm$ (Given) $\angle OCP=\frac{\angle ACP}{2}={30}^{\circ }$.

$PC=\frac{BC}{2}=3cm$

in $\Delta OPC$ :-

$\cos \angle OCP=\frac{PC}{OC}$

$\Rightarrow \cos {30}^{\circ }=\frac{PC}{OC}$

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{3}{OC}$

$\Rightarrow OC=2\sqrt{3}cm$

$\therefore$ Radius of circle $OC=2\sqrt{3}$ cm