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Trigonometric Ratios of Compound Angles

In a triangle...

Question

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

A

c +a

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B

a + b + c

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C

a + b

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D

b + c

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Solution

The correct option is C
a + b

Given, $∠ C = \frac{π}{2} ∵ \frac{c}{s i n C} = 2 R \Rightarrow 2 R = c a n d r = (s - c) t a n \frac{C}{2} = s - c ∴ 2 r + 2 R = 2 s - 2 c + c \Rightarrow 2 (r + R) = a + b$

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