Let A B C be a triangle such that A B = 15 and A C = 9 . The bisector of ∠ B A C meets B C in D . If ∠ A C B = 2 ∠ A B C , then B D is

Question

Let A B C be a triangle such that A B = 15 and A C = 9 . The bisector of ∠ B A C meets B C in D . If ∠ A C B = 2 ∠ A B C , then B D is, 8, 9, 10, 12

MARKS App · Accepted Answer

In ∆ A B C 15 sin 2 θ = 9 sin θ = BC sin 3 θ 15 sin ⁡ 2 θ = 9 sin ⁡ θ ⇒ cos ⁡ θ = 5 6 9 sin ⁡ θ = BC sin ⁡ 3 θ ⇒ BC = 9 3 − 4 sin 2 ⁡ θ = 9 4 cos 2 ⁡ θ − 1 = 9 4 × 25 36 − 1 = 16 ∴ BD = 5 8 BC = 10

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