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AP EAMCET201825 Apr 2018Morning ShiftMathematicsStraight LinesActual

The circumcentre of the triangle with vertices at ( - 2 , 3 ) , ( 1 , - 2 ) and ( 2 , 1 ) is

Options

  1. A6 7 , 2 7
  2. B- 6 7 , 2 7
  3. C6 7 , - 2 7
  4. D- 6 7 , - 2 7

Correct answer

B. - 6 7 , 2 7

Step-by-step solution

Circumcentre of the triangle is equidistant from the vertices of the triangle. Let O x , y be the circumcentre of the triangle. Now, O A = x + 2 2 + y - 3 2     . . . i O B = x - 1 2 + y + 2 2     . . . ii O C = x - 2 2 + y - 1 2     . . . iii O A = O B = O C Equating i   &   ii , we get x + 2 2 + y - 3 2 = x - 1 2 + y + 2 2 ⇒ x + 2 2 + y - 3 2 = x - 1 2 + y + 2 2 3 x - 5 y + 4 = 0     . . . iv Equating ii   &   iii , we get x - 1 2 + y + 2 2

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