What is Stewart's Theorem?

Answer 1

Stewart's theorem concerns the relationship between the lengths of a triangle's sides and a cevian. A cevian is a straight line from a vertex to the opposite side. Suppose you have a triangle whose sides are of length x, y and z. Suppose the cevian, of length a, divides the side of length x into segments of lengths p and q (with p nearer to y and q nearer to z.Then, according to Stewart's theorem,y^2*q + z^2*r = x*(a^2 + pq)