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AP EAMCET202319 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , if r is the inradius and r ₁, r ₂, r ₃ are the ex-radii, then 1 4 [b^2 2 C+c^2 2 B ]=

Options

  1. Arr ₁ A 2
  2. Bb c A
  3. Crr ₁ r ₂ r ₃
  4. Drr ₁ A 2

Correct answer

D. rr ₁ A 2

Step-by-step solution

1 4 [b^2 2 C+c^2 2 B ] aligned & = 1 4 [b^2 2 C C+c^2 2 B B ] & = 1 2 [b^2 C 2 a b +c^2 B 2 c a ] [ A= 2 b c ] & = a [b C+c B]= [ a=b C+c B] & r r₁ A 2 = s s-a s(s-a) = & 1 4 [b^2 2 C+c^2 2 B ]=r r₁ A 2 aligned

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