Let $\angle A$ be given with two sides $l_1,l_2$, and a point $K$ in the interior of the angle. How could I construct two points $p_1,p_2$ on $l_1,l_2$ respectively, so that the midpoint of $p_1$ and $p_2$ is exactly $K$?
I don't know where to start. I thought of constructing a perpendicular bisector of $AK$, but that has nothing to do with the two sides of the angle. Then I thought of constructing the angle bisector of $A$, but it need not pass $K$. Any suggestions?