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MHT CET202014 Oct 2020Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations, if A , B , C are in H.P., then a², b², c² are in

Options

  1. AA _ n P .
  2. BNot in A. P.
  3. CH . P
  4. DG . P

Correct answer

A. A _ n P .

Step-by-step solution

If A, B, C are in H.P., then 2 B = 1 A + 1 C 2 B B = A A + C C We know that a A = b B = c C 2 ( a²+c²-b² 2 a c ) b k = b²+c²-a² 2 b c a k + a²+b²-c² 2 a b 2 (c²+a²-b² ) 2 a b c k = b²+c²-a² 2 a b c k + a²+b²-c² 2 a b c k 2 (a²+c²-b² )=b²+c²-a²+a²+b²-c²2 a²+2 c²-2 b²=2 b² 4 b²=2 a²+2 c² 2 b²=a²+c² a², b², c² a r e in A P .

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