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AP EAMCET201922 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

In ( A B C, 1 r₁^2 + 1 r₂^2 + 1 r₃^2 + 1 r^2 = )

Options

  1. A( a^2+b^2+c^2 ^2 )
  2. B( a+b+c ^2 )
  3. C( s^2 ^2 )
  4. D( 4 s^2 ^2 )

Correct answer

A. ( a^2+b^2+c^2 ^2 )

Step-by-step solution

( ) (r₁= s-a ) ( ) ( 1 r₁ = s-a ) Similarly, ( 1 r₂ = s-b 1 r₃ = s-c ) and ( 1 r = s ) Now, ( 1 r₁^2 + 1 r₂^2 + 1 r₃^2 + 1 r^2 ) ( aligned & = (s-a)^2 ^2 + (s-b)^2 ^2 + (s-c)^2 ^2 + s^2 ^2 & = s^2+a^2-2 a s+s^2+b^2-2 s b+s^2+c^2-2 s c+s^2 ^2 & = 4 s^2+a^2+b^2+c^2-2 s(a+b+c) ^2 & = 4 s^2+a^2+b^2+c^2-4 s^2 ^2 = a^2+b^2+c^2 ^2 aligned )

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