What is the name of this result about isosceles triangles?

$\Delta ABC$ is isosceles with $AB=AC=p$. $D$ is a point on $BC$ where $AD=q$, $BD=u$ and $CD=v$.

Then the following holds.

$$p^2=q^2+uv$$

I would like to know whether this result has a name.

Stewart's theorem

Let $a$, $b$, and $c$ are the length of the sides of the triangles. Let $d$ be the length of the cevian to the side of length $a$.  If the cevian divides the side of length $a$ into two segments of length $m$ and $n$ with $m$ adjacent to $c$ and $n$ adjacent to $b$, then Stewart's theorem states that $b^2m +c^2n=a(d^2+mn)$

Note

Apollonius's theorem is a special case of this theorem.

Edit: I forgot some factors $\frac{1}{2}$.

Derivation: $$h^2 = p^2 - \frac{1}{4}(u+v)^2\ ,$$ $$q^2 = h^2 + \frac{1}{4}(u-v)^2\ ,$$ where $h$ is the height perpendicular to $BC$. Therefore, $$p^2 = h^2 + \frac{1}{4}(u+v)^2 = q^2 - \frac{1}{4}(u-v)^2 + \frac{1}{4}(u+v)^2 = q^2 + uv\ .$$ I don't know if it has a name, but it is certainly a nice formula!