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MHT CET202124 Sep 2021Morning ShiftMathematicsProperties of TrianglesActual

With usual notations in A B C , if A C = (A-B) (B-C) , then a ^2, ~b ^2, c ^2 are in

Options

  1. ANot in AP
  2. BHP
  3. CAP
  4. DGP

Correct answer

C. AP

Step-by-step solution

aligned & A C = (A-B) (B-C) & A( B C- B C)= A B- A B) & A B C + A B C =2 A B C & B ( A C + A C )=2 A B C & B [ [ A + C ]=2 A B C & B B =2 A B C [ A + B + C = ] & 1 2 B = A B C B & By sine rule, we know that a A = b B = c C & 1 2 ( c ^2+ a ^2- b ^2 2 ac ) = a b a c ac c ^2+ a ^2- b ^2 = ac b ^2 & c ^2+ a ^2- b ^2= b ^2 2 ~b ^2= a ^2+ c ^2 & aligned

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