The radii of the escribed circles of triangle A B C are ra , rb and rc respectively. If ra+rb=3 R and rb+re=2 R, then the smallest angle of the triangle is

Question

The radii of the escribed circles of triangle A B C are ra , rb and rc respectively. If ra+rb=3 R and rb+re=2 R, then the smallest angle of the triangle is (A)  tan -1(√2-1) (B) (1/2) tan -1(√3) (C) (1/2) tan -1(√2+1) (D)  tan -1(2-√3)

Tardigrade Admin · Accepted Answer

Correct answer is (b) (1/2) tan -1(√3)

Q. The radii of the escribed circles of $△ A BC$ 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

$tan^{- 1} (2 - 1)$

$\frac{1}{2} tan^{- 1} (3)$

$\frac{1}{2} tan^{- 1} (2 + 1)$

$tan^{- 1} (2 - 3)$

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

Q. The radii of the escribed circles of △ABC are ra​,rb​ and rc​ respectively. If ra​+rb​=3R and rb​+re​=2R, then the smallest angle of the triangle is

tan−1(2​−1)

21​tan−1(3​)

21​tan−1(2​+1)

tan−1(2−3​)