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Q.

In a triangle ABC , Let $C = \frac{π}{2}$ .If r is the in radius and R is circum radius of the triangle then 2(r+R) is equal

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a

a+b

b

b+c

c

c+a

d

a+b+c

answer is A.

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Detailed Solution

$\begin{array}{l} ∠ C = 90^{\circ} \\ c = 2 Rsin c = 2 R \\ c = 2 R \\ r = (s - c) \tan \frac{c}{2} \\ r = (s - c) (1) \\ r = s - c \\ 2 r = 2 s - 2 c \\ 2 r = a + b + c - 2 c = a + b - c \\ 2 r + c = a + b 2 r + 2 R = a + b 2 (r + R) = a + b \end{array}$

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