Stewart's Theorem

Theorem
Let $\triangle ABC$ be a triangle with sides $a, b, c$.

Let $CP$ be a cevian from $C$ to $P$.


 * Stewart's Theorem.png

Then:


 * $a^2 \cdot AP + b^2 \cdot PB = c \paren {CP^2 + AP \cdot PB}$

Proof
It is also known as Apollonius's Theorem after.