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AP EAMCET202317 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In A B C , if (a-b)(s-c)=(b-c)(s-a) , then r₁, r₂, r₃ are in

Options

  1. AArithmetic progression
  2. BGeometric progression
  3. CHarmonic progression
  4. DArithmetico - geometric progression

Correct answer

A. Arithmetic progression

Step-by-step solution

Given: (a-b)(s-c)=(b-c)(s-a) aligned & [(s-a)-(s-b)](s-c)=[(s-b)-(s-c)](s-a) & (s-a)(s-c)-(s-b)(s-c) & =(s-b)(s-a)-(s-c)(s-a) aligned Dividing by (s-a)(s-b)(s-c) on both sides, we get aligned & 1 (s-b) - 1 (s-a) = 1 (s-c) - 1 (s-b) & 2 (s-b) = 1 (s-a) + 1 (s-c) & 2 (s-b) = (s-a) + (s-c) & 2 r₂=r₁+r₃ aligned So, r₁, r₂, r₃ are in arithmetic progression.

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