Information About

Symmedian Point




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A triangle with medians (blue), angle bisectors (green) and symmedians (red). The symmedians intersect in the Lemoine point L.


The symmedian point of a triangle with sides ''a'', ''b'' and ''c'' has homogeneous Trilinear Coordinates : ''b'' : ''c'' .

The symmedian point ''L'' can also be constructed differently: the three lines joining the midpoint of a side to the midpoint of the Altitude on that side intersect in ''L''. The symmedian point of a Right Triangle is therefore the midpoint of the altitude on the hypotenuse.

The Gergonne Point of a triangle is the same as the symmedian point of the triangle's Contact Triangle .

The symmedian point is the Isogonal Conjugate of the triangle's Centroid .


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