Stewart's theorem

In geometry, Stewart's theorem yields a relation between the lengths of the sides of the triangle and the length of a cevian of the triangle. Its name is in honor of the Scottish mathematician Matthew Stewart who published the theorem in 1746.

Let ${\displaystyle a}$, ${\displaystyle b}$, and ${\displaystyle c}$ be the lengths of the sides of a triangle. Let ${\displaystyle d}$ be the length of a cevian to the side of length ${\displaystyle a}$. If the cevian divides ${\displaystyle a}$ into two segments of length ${\displaystyle m}$ and ${\displaystyle n}$, with ${\displaystyle m}$ adjacent to ${\displaystyle c}$ and ${\displaystyle n}$ adjacent to ${\displaystyle b}$, then Stewart's theorem states that

...
Wikipedia