Question

In a ∆ABC, let ∠C= $\frac { \pi } { 2 }$ . If r and R are the inradius and the

circumradius respectively of the triangle then 2(r + R) is equal

to –

• A. a + b
• B. b + c
• C. c + a
• D. a + b + c

Answer 1

Answer: (A)

a + b

Answer 2

Here, R = OA = OB = OC = $\frac { 1 } { 2 }$ AB = $\frac { \mathrm { c } } { 2 }$

r = $\frac { \Delta } { \mathrm { s } }$ = =

∴ r + R = $\frac { a b } { a + b + c }$ + $\frac { \mathrm { c } } { 2 }$

= $\frac { 2 a b + c ( a + b + c ) } { 2 ( a + b + c ) }$

= (Q c² = a² + b²)

= =

∴ 2 (r + R) = a + b