If-in-a-ABC-8R-2-a-2-b-2-c-2-then-the-ABC-is-

Question Number 95512 by bagjamath last updated on 25/May/20

If in a △ A B C, 8 R^{2} = a^{2} + b^{2} + c^{2}, then

the △ A B C is

Commented by som(math1967) last updated on 25/May/20

Rt angle triangle

Commented by som(math1967) last updated on 25/May/20

a^{2} + b^{2} + c^{2} = {8 R}^{2}

{4 R}^{2} (\sin^{2} A + \sin^{2} B + \sin^{2} c) = {8 R}^{2}

{2 \sin}^{2} A + {2 \sin}^{2} B + {2 \sin}^{2} C = 4

\cos 2 A + \cos 2 B + {2 \cos}^{2} C = 0

2 \cos (A + B) \cos (A - B) + {2 \cos}^{2} C = 0

- cosCcos (A - B) + \cos^{2} C = 0 ★

- cosC {\cos (A - B) - \cos (A + B) = 0 ★

2 cosCcos Acos B = 0

eithercos C = 0 / cosB = 0 / cosA = 0

∴ ∠ C = 90 or ∠ B = 90 or ∠ A = 90

★ \cos (A + B) = \cos (π - C) = - cosC

Commented by bagjamath last updated on 25/May/20

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