Let $ABCD$ a tetrahedron and $H_1$, $H_2$ the intersections of the altitudes in the triangles $BCD$ and $ACD$. If $A, B, H_1, H_2$ are coplanar show that $ABH_1H_2$ are concyclic.
I noticed that the foot of the altitude from $A$ in $\triangle ACD$ is the same as the foot of the altitude from $B$ in $\triangle BCD$. Also, $AB\perp CD$. I draw $AO_1 \perp (BCD)$ and $BO_2 \perp (ACD)$. Then $A, O_2, H_2$ are on the same line and $B, O_1, H_1$ are on the same line. Now I have to show that $O_1O_2||H_1H_2$ and I have no idea to continue.