Question

The radii of the escribed circles of $\triangle A B C$ are $r_{a }, r_b$ and $r_c$ respectively. If $r_a+r_b=3 R$ and $r_b+r_e=2 R$, then the smallest angle of the triangle is

• A. $\tan ^{-1}(\sqrt{2}-1)$
• B. $\frac{1}{2} \tan ^{-1}(\sqrt{3})$
• C. $\frac{1}{2} \tan ^{-1}(\sqrt{2}+1)$
• D. $\tan ^{-1}(2-\sqrt{3})$

Answer 1

Answer: (B)

Correct answer is (b) $\frac{1}{2} \tan ^{-1}(\sqrt{3})$