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Question

If (α, β), (¯x  , ¯y) and (u, v)are respectively coordinates of the circumcentre, centroid and orthocentre of a triangle.
  1. 3
  2. 3
  3. 3
  4. 3


Solution

The correct option is D 3
We know that, the centroid of a triangle divides the segment joining the orthocentre and circumcentre internally in the ratio 2 : 1. Therefore,
¯x=2α+u2+1and¯y=2β+v2+1
3¯x=2α+uand¯y=2β+v

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