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AP EAMCET202420 May 2024Evening ShiftMathematicsProperties of TrianglesActual

In A B C, b c-r₂ r₃=

Options

  1. Ar r₁
  2. Br₂
  3. Cr₁
  4. Da r₁

Correct answer

A. r r₁

Step-by-step solution

r r₁+r₂ r₃= s s-a + s-b s-c aligned & = ^2[(s-b)(s-c)+s(s-a)] s(s-a)(s-b)(s-c) & =(s-b)(s-c)+s(s-a) & [ = s(s-a)(s-b)(s-c) ] & =s^2-s(b+c)+b c+s^2-s a & =2 s^2-s(a+b+c)+b c [ 2 s=a+b+c] & =2 s^2-2 s^2+b c & r r₁+r₂ r₃=b c r r₁=b c-r₂ r₃ aligned

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