Question

If R is the radius of the circumcircle of the $\triangle A B C$ and $\Delta$ is its area, then

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

Answer 1

Answer: (C)

$R = \frac { a b c } { 4 \Delta }$

Answer 2

Area of the triangle $A B C ( \Delta ) = \frac { b c } { 2 } \sin A$. From the sine

formula, $a = 2 R \sin A$ or $\sin A = \frac { a } { 2 R }$ ⇒ $\Delta = \frac { 1 } { 2 } b c \cdot \frac { a } { 2 R } = \frac { a b c } { 4 R }$

or $R = \frac { a b c } { 4 \Delta }$ .