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BITSAT2018MathematicsSequences and SeriesActual

If a , b , c are in GP and log a - log 2 b , log 2 b - log 3 c and log 3 c - log a are in AP , then a , b and c are the lengths of the sides of a triangle, which is

Options

  1. Aequilateral
  2. Bright angled
  3. Cacute-angled
  4. Dobtuse angled

Correct answer

D. obtuse angled

Step-by-step solution

Given, a ,   b ,   c are in GP . ∴   b 2 = a c and 2 log 2 b - log 3 c = log a - log 2 b + log 3 c - log a ⇒ b 2 = a c and 2 b = 3 c ∵   a + b = 5 a 3 > c ,   b + c = 10 a 9 > a and c + a = 13 a 9 > b ∴   a ,   b ,   c are the sides of a triangle. Also, a is the greatest side ∴   cos A = b 2 + c 2 - a 2 2 b c = - 29 48 < 0 ∴   ∆ ABC is an obtuse angled triangle. Hence, option (d) is correct.

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