In a triangle ABC, let $∠C=\frac{π}{2}$. If r is the inradius and R is the circumradius of the triangle, then 2(r + R) is equal to:
Answer & explanation
Correct answer: option 1
$\frac{c}{\sin C}=2R⇒c=2R$ [as C = 90°] Also $r=(s-c)\tan\frac{C}{2}=(s-c)$ [∵ tan 45° = 1]
⇒ 2r = 2s - 2c ⇒ 2r = a + b + c - 2c ⇒ 2r = a + b - c = a + b - 2R
⇒ 2(r + R) = a + b