Question: In a triangle ABC, let $\angle C = \frac { \pi } { 2 }$. If r is the in radius and R is the circum...

Question

In a triangle ABC, let $\angle C = \frac { \pi } { 2 }$ . If r is the in radius and R is the circum-radius of the triangle, then $2 ( r + R )$ is equal to

Answer 1

Solution

$\frac { c } { \sin C } = 2 R$ , ∴ $c = 2 R \sin 90 ^ { \circ } = 2 R$

Also $r = ( s - c ) \tan \frac { C } { 2 } = ( s - c )$ $\left[ \because \tan 45 ^ { \circ } = 1 \right]$

$2 r = 2 s - 2 c = a + b - c = a + b - 2 R$ , $2 ( r + R ) = a + b$ .

Question: In a triangle ABC, let \(\angle C = \frac { \pi } { 2 }\). If r is the in radius and R is the circum...

Solution