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Manipal MET2024MathematicsProperties of Triangles

If in a A B C, ^2 A+ ^2 B+ ^2 C=2 , then the triangle is always:

Options

  1. Aisosceles triangle
  2. Bright angled
  3. Cacute angled
  4. Dobtuse angled

Correct answer

B. right angled

Step-by-step solution

^2 A+ ^2 B+ ^2 C=2= 1- 2 A 2 + 1- 2 B 2 + 1- 2 C 2 =2 2 A+ 2 B+ 2 C=-1 2 (A+B) (A-B)=-2 ^2 C 2 ( -C) (A-B)=-2 ^2 C [ A+B+C= ] 2 C[ C- (A-B)]=0 -2 C[ (A+B)+ (A-B)]=0 - A B C=0 A B C=0 Therefore, one of them should be equal to zero. So, exactly one angle is 90^ .

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