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AP EAMCET202422 May 2024Evening ShiftMathematicsProperties of TrianglesActual

In a ABC , if r: R : r₂=1: 3: 7 then ( A + C )+ B =

Options

  1. A0
  2. B3
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

Let r= k , R =3 k and r₂=7 k aligned & r₂-r=4 R ~A 2 ~B 2 C 2 -4 R ~A 2 ~B 2 C 2 & 7 k - k =4 R ~B 2 [ ~A 2 C 2 - A 2 C 2 ] & 6 k =12 k ~B 2 ( ~A + C 2 ) [ A + B + C = ] & 1 2 = B 2 ( 2 - B 2 )= ^2 ~B 2 ~B 2 = 1 2 ~B =90^ aligned aligned & Now, (A+C)+ B= ( -B)+ B & =2 B=2 90^ =2 aligned

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