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AP EAMCET201825 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In Δ A B C , r 1 - r a + r 2 - r b + r 3 - r c =

Options

  1. Ar 1 + r 2 + r 3 s
  2. Br 1 + r 2 + r 3 2 s
  3. Cr 1 + r 2 + r 3 2
  4. Dr 1 + r 2 + r 3 3 s

Correct answer

A. r 1 + r 2 + r 3 s

Step-by-step solution

We have, r 1 - r a + r 2 - r b + r 3 - r c ⇒ 1 a ∆ s - a - ∆ s + 1 b ∆ s - b - ∆ s + 1 c ∆ s - c - ∆ s = ∆ s s - a + ∆ s s - b + ∆ s s - c = r 1 s + r 2 s + r 3 s = r 1 + r 2 + r 3 s

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