Question

In a triangle ABC, Let , $\angle C=\frac{\pi }{2}$, if r is the inradius and R is the circumradius of the triangle ABC, then 2(r+R) equals

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

Answer 1

The correct option is C

a + b

Given, $\angle C=\frac{\pi }{2}\because \frac{c}{sinC}=2R\Rightarrow 2R=candr=(s-c)tan\frac{C}{2}=s-c\therefore 2r+2R=2s-2c+c\Rightarrow 2(r+R)=a+b$