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AP EAMCET201920 Apr 2019Evening ShiftMathematicsProperties of TrianglesActual

Let denote the area of a A B C . If , , are the lengths of the altitudes of the A B C , then ⁻²+ ⁻²+ ⁻²=

Options

  1. A4 ( A+ B+ C)
  2. B1 ( A+ B+ C)
  3. C^2 2 ( A+ B+ C)
  4. D^2 4 ( A+ B+ C)

Correct answer

B. 1 ( A+ B+ C)

Step-by-step solution

aligned & Since, ⁻²+ ⁻²+ ⁻²= a^2 4 ^2 + b^2 4 ^2 + c^2 4 ^2 & = a^2+b^2+c^2 4 ^2 & = (a^2+b^2-c^2 )+ (b^2+c^2-a^2 )+ (c^2+a^2-b^2 ) 4 ( a b c 4 R )^2 & = 2 a b C+2 b c A+2 a c B a^2 b^2 c^2 4 R^2 & = C ( a b c 4 R ) c 2 R + A ( a b c 4 R ) a 2 R + B ( a b c 4 R ) b 2 R & = 1 ( A+ B+ C) aligned Hence, option (b) is correct.

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