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AP EAMCET2016MathematicsProperties of Triangles

In ABC , if the sides a, b, c are in geometric progression and the largest angle exceeds the smallest angle by 60^ , then B is equal to

Options

  1. A13 +1 4
  2. B1- 13 4
  3. C1
  4. D13 -1 4

Correct answer

D. 13 -1 4

Step-by-step solution

In ABC , sides a, b and c are in GP. b^2=a c .( i ) Given, largest angle exceeds the smallest angle by 60^ . aligned & C - A =60^ . (ii) & ( C - A )= 60^ & C A + C A = 1 2 aligned We know, a A = b B = c C =k aligned & 2 C A +2 C A =1 & ( C + A )+ ( C - A )+2 k^2 a c=1 & ( + B )+ 60^ +2 k^2 b^2=1 [ a c=b^2 ] & - B + 1 2 +2 ^2 ~B =1 [ b k= B ] & - B +1+4 ^2 ~B =2 & -2 B +1+4 (1- ^2 ~B )=2 & 4 ^2 ~B +2 B -3=0 & B = -2 4+48 2 4 = -2 2 13 8 & = 13 -1 4 or - 13 -1 4 aligned

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