How to construct $\Delta ABC$ given $a$, height from $A$ on $BC$ and A$B:AC$.

Question

How to construct $\Delta ABC$ given $a$, height from $A$ on $BC$ and A$B:AC$.

Answer 1

If the ratio $\frac{AB}{AC}$ is known, then $A$ belong to an Apollonius circle relative to the segment $BC=a$, hence the problem can be solved by intersecting a line parallel to $BC$ with the previous circle. Here it is an explicit solution for $BC=4$, $\frac{AB}{AC}=\frac{2}{3}$ and $h_a=3$: