A median of a triangle is the Cevian from one of its vertices to the midpoint of the opposite side. The three medians of any triangle are concurrent (Casey 1888, p. 3), meeting in the triangle centroid (Durell 1928) , which has trilinear coordinates . In addition, the medians of a triangle divide one another in the ratio 2:1 (Casey 1888, p. 3). A median also bisects the area of a triangle.
Let denote the length of the median of the th side . Then
(1)
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(2)
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(Casey 1888, p. 23; Johnson 1929, p. 68). The area of a triangle can be expressed in terms of the medians by
(3)
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where
(4)
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