Question

If $R$ is the radius of the circumcircle of the $\Delta ABC$ and $\Delta$ is its area, then

• A. $R=\frac{a+b+c}{\Delta }$
• B. $R=\frac{a+b+c}{4\Delta }$
• C. $R=\frac{abc}{4\Delta }$
• D. $R=\frac{abc}{\Delta }$

Answer 1

Answer: (C)

$R=\frac{abc}{4\Delta }$

$\frac{\sin A}{a}=\frac{1}{2R}$

$\Rightarrow R=\frac{a}{2\sin A}$

$=\frac{a}{2.\frac{2△}{bc}}$

$=\frac{abc}{4△}.$

Hence, the answer is $\frac{abc}{4△}.$