The ratios of the lengths of the sides BC and A C of a triangle A BC to the radius of a circumscribed circle are equal to 2 and 3/2 respectively. If the ratio of the lengths of the bisectors of the in

Question

The ratios of the lengths of the sides BC and A C of a triangle A BC to the radius of a circumscribed circle are equal to 2 and 3/2 respectively. If the ratio of the lengths of the bisectors of the interior angles B and C is α ( 9 β ​ α ​ − 1 ​ ) then α + β is

TestHub · Accepted Answer

Given R a ​ = 2 ; R b ​ = 2 3 ​ 2 a ​ = 3/2 b ​ = R CF BE ​ = a + b 2 ab ​ c o s 2 c ​ a + c 2 a c ​ c o s 2 B ​ ​ = a + c a + b ​ ⋅ c o s 2 C ​ c o s 2 B ​ ​ ⋅ b c ​ . …………… ( 1 ) ∵ a = 2 R use here a 2 = b 2 + c 2 ⇒ c = 2 7 ​ R ​ sin B = 4 3 ​ ; sin = 4 7 ​ ​ cos 2 2 B ​ = 2 4 + 7 ​ ​ ; cos 2 2 B ​ = 2 4 + 7 ​ ​ ; cos 2 2 c ​ = 8 7 ​ Now from ........................(1) CF BE ​ = 9 2 ​ 7 ( 7 ​ − 1 ) ​

Mathematics - Properties of Triangle Question with Solution | TestHub

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JEE Advanced 2028 (Class 11)