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BITSAT2009MathematicsHeights and DistancesActual

In a triangle ( ABC , C =90^ ), then ( a^2-b^2 a^2+b^2 ) is equal to :

Options

  1. A( ( A + B ) )
  2. B( (A-B) )
  3. C( ( A + B ) )
  4. D( ( A - B 2 ) )

Correct answer

B. ( (A-B) )

Step-by-step solution

( aligned & A + B =180^ - C =90^ & a =2 R A , b=2 R B , c=2 R C & array l a^2-b^2 a^2+b^2 = ^2 ~A - ^2 ~B ^2 ~A + ^2 ~B = ( A + B ) ( A - B ) ^2 ~A + ^2 (90^ - A ) [ A + B =90^ ] = 90^ ( A - B ) ^2 ~A + ^2 ~A = ( A - B ) array aligned )

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