For the triangle in the picture, coordinates of $A$, $B$ and $C$ are known. Is there an explicit formula for length $XY$, as a function of height $h$? It's a function of other variables as well, but it's important that it depends explicitly on $h$.
$XY$ is parallel to side $c$, but I'm not good at drawing.
$Cxy$ is similar to $CAB$, so the sides are in the same ratio as the altitudes.