Stewart's Theorem relates the length of a cevian, a line segment from a vertex of a triangle to a point on the opposite side, to the lengths of the triangle's sides and the two segments the cevian creates on that side. Named for Matthew Stewart, it is a classical tool of triangle geometry that generalizes the formulas for a triangle's medians and angle bisectors into a single relation.
Facts
StatementFor a triangle with side lengths a, b and c, and a cevian of length d to the side of length a dividing it into segments m (adjacent to c) and n (adjacent to b), Stewart's theorem states that b squared times m plus c squared times n equals a times the quantity d squared plus m times n. 1 Classification
Statement Form Connections
Sources
1. Stewart's Theorem (Wikipedia)
Wikimedia Foundationopening paragraph, first sentence
In geometry, Stewart's theorem yields a relation between the lengths of the sides and the length of a cevian in a triangle.
opening paragraph, second sentence
Its name is in honour of the Scottish mathematician Matthew Stewart, who published the theorem in 1746.
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