When Is a Quadrilateral Cyclic?

Problem!

As David showed before, right angles create cyclic quads. Let $ABC$ be a right triangle, where $K, L,$ and $M$ are the feet of the $A$-, $B$-, and $C$-heights, respectively, and $H$ is the orthocenter of $\triangle ABC$. Find 6 cyclic quadrilaterals. (I will only provide a solution below to check)