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In geometry, the symmedian point, Lemoine point or Grebe point is the intersection of the three symmedians of a triangle.
Ross Honsberger called its existence "one of the crown jewels of modern geometry".
In the Encyclopedia of Triangle Centers the symmedian point appears as the sixth point, X. For a non-equilateral triangle, it lies in the open orthocentroidal disk punctured at its own center, and could be any point therein.
The symmedian point of a triangle with side lengths a, b and c has homogeneous trilinear coordinates.
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