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AP EAMCET202120 Aug 2021Morning ShiftMathematicsProperties of TrianglesActual

In a Δ A B C , 2 Δ 2 = a 2 b 2 c 2 a 2 + b 2 + c 2 , then the triangle is

Options

  1. AEquilateral
  2. BIsosceles
  3. CRight angled
  4. DAcute angled triangle

Correct answer

C. Right angled

Step-by-step solution

We have, 2 Δ 2 ( a 2 + b 2 + c 2 ) = a 2 b 2 c 2   ⇒ ( a 2 + b 2 + c 2 ) = ( a b c Δ ) 2 . 1 2 = 8 R 2   ⇒ sin 2 A + sin 2 B + sin 2 C = 2   ⇒ cos 2 A + cos 2 B + cos 2 C = − 1   ⇒ − 1 −   4 cos A cos B cos C = − 1   ∴ cos A cos B cos C = 0   ⇒ cos a = 0   or   cos B = 0   or   cos C = 0   Therefore, any one of the angle is 90 ° , hence, it is a right angled triangle

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