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Question: In a∆ABC, let ∠C= \(\frac { \pi } { 2 }\). If r and R are the inradius and the circumradius respect...

In a∆ABC, let ∠C= π2\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

a + b

Explanation

Solution

Here, R = OA = OB = OC = 12\frac { 1 } { 2 } AB =

r = = =

∴ r + R = +

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

= (Q c2 = a2 + b2)

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

∴ 2 (r + R) = a + b