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AP EAMCET202418 May 2024Morning ShiftMathematicsStraight LinesActual

In H is orthocentre of ABC and AH =x ; BH =y ; CH =z then a b c x y z =

Options

  1. A1
  2. Ba+b+c x+y+z
  3. Ca x + b y + c z
  4. Da b+b c+c a x y+y z+z x

Correct answer

C. a x + b y + c z

Step-by-step solution

Given H is orthocentre of A B C and AH =x, BH =y, CH =z Since, AH =2 R A =x BH =2 R B =y CH =2 R c=z Now, a b c x y z = a b c 2 R A 2 R B 2 R C aligned & = a 2 R b 2 R c 2 R 1 A B C & = A B C A B C = A B C aligned aligned & = A+ B+ C & = A A + B B + C C aligned = a 2 R A + b 2 R B + c 2 R C = a x + b y + c z

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