In an elliptic billiard, there is a triangular orbit that starts from any point on the ellipse.
1) How to find such orbits with straightedge and compass?
2) Is it possible to construct a triangle given its symmedian point $K$, the feet $H_A$ of the altitude from the vertex $A$ and the point $J_A$ of intersection between the $BC$-line and the $H_B H_C$-line?
A solution to the second question solves the first one, too.
