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AP EAMCET202315 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , if 1 r ₁ , 1 r ₂ and, 1 r ₃ are in arithmetic progression, then r ₂: r =

Options

  1. A3: 2
  2. B2: 1
  3. C1: 3
  4. D3: 1

Correct answer

D. 3: 1

Step-by-step solution

1 r₁ , 1 r₂ , 1 r₃ are in arithmetic progression Then, 2 r₂ = 1 r₁ + 1 r₃ aligned & 2(s-b) - = s-a + s-c & 2(s-b)=2 s-(a+c) & 2 s-2 b=2 s-(a+c) 2 b=a+c aligned Now, r₂ r₁ = s-b s = s s-b = 2 s 2 s-2 b = a+b+c a+b+c-2 b = 2 b+b a+c-b = 3 b 2 b-b = 3 b b r₂ r = 3 1

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