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AP EAMCET201822 Apr 2018Evening ShiftMathematicsStraight LinesActual

The orthocentre and the centroid of A B C are (5,8) and (3, 14 3 ) respectively. The equation of the side B C is x-y=0 . Given that the image of the orthocentre of a triangle with respect to any side lies on the circumcircle of that triangle, then the diameter of the circumcircle of A B C is

Options

  1. A10
  2. B2 10
  3. C4 10
  4. D8 10

Correct answer

C. 4 10

Step-by-step solution

The centroid on a non-equilateral triangle divides the line joining orthocentre and circumcentre in 2: 1 , so let the coordinates of circumcentre is (h, k) , then array rlrl & & ( 2 h+5 3 , 2 k+8 3 )= (3, 14 3 ) & h=2 k=3 array And image of orthocentre (5,8) with respect to side B C, x-y=0 is (8,5) So, the radius of circumcircle of A B C is (8-2)^2+(5-3)^2 = 40 Then diameter =4 10 .

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