Trigonometric EquationHard

Question

In a triangle ABC, let ∠C = π / 2 If r is the inradius and R is the circumradius of the triangle, then 2 (r + R) is equal to

Options

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

Solution

       
Here, R2 = MC2 = (a2 + b2) (by distance from origin)
              (Pythagorus theorem)
⇒     R =
Next, r = (s - c) tan(C / 2) = (s - c) tan π / 4 = s - c
∴     2(r + R) = 2r + 2R = 2s - 2c + c
      = a + b + c - c = a + b

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