Question

Radius of the circum circle of $△LMN$ is:

• A. $2R$
• B. $R$
• C. $\frac{R}{2}$
• D. $\frac{R}{4}$

Answer 1

The correct option is C $\frac{R}{2}$

Let $R^{\prime }$ be the circumradius of $△LMN$ then
$R^{\prime }=\frac{MN}{2\sin \angle MLN}$
$=\frac{a\cos A}{2\sin (\pi -2A)}$
$=\frac{2R\sin A\cos A}{2\sin 2A}$
$=\frac{2R\sin A\cos A}{2\times 2\sin A\cos A}$
$=\frac{R}{2}$ (on simplification)