In triangle A B C , if B C is the hypotenuse, then r 2 + r 3 =

Question

In triangle A B C , if B C is the hypotenuse, then r 2 + r 3 =, r 1 + r, a, r - r 1, 2 R + r

MARKS App · Accepted Answer

Since, B C is the hypotenuse, so triangle is right-angled at A , therefore ∠ A = π 2 . Now, we have, r 2 + r 3 = Δ s - b + Δ s - c = Δ 2 s - b - c s - b s - c × s s - a s s - a = Δ a s s - a Δ 2 = a s s - a Δ = a tan A 2 = a tan 45 ° = a ∵ A = π 2

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