NL-NWO 1972 Problem 5

Given is an acute-angled triangle $ABC$ with angles $\alpha$ , $\beta$ and $\gamma$ . On side $AB$ lies a point $P$ such that the line connecting the feet of the perpendiculars from $P$ on $AC$ and $BC$ is parallel to $AB$ . Express the ratio $\frac{AP}{BP}$ in terms of $\alpha$ and $\beta$ .