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The orthocentre and the centroid of ΔABC are (5,8) 3,143 respectively. The equation of the side BC 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 ΔABC is

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a

10

b

210

c

410

d

810

answer is C.

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Detailed Solution

O(5,8)G3,143S(α,β) is circumcentreG is divides OS in the ratio 2:1S(α,β)=(2,3)Image O (5,8) w.r.t line y=x is A (8,5)∴ Point A is lies on circleradius of circle r=AS=40Diameter of circle 2r=410
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The orthocentre and the centroid of ΔABC are (5,8) 3,143 respectively. The equation of the side BC 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 ΔABC is