Maximum number of right-angled triangles

For 5 points the maximal number of right triangles is 7.

In the following figure, $\phi$ is the golden ratio. Drop two and one of the extremal points to obtain 12 and 16 right triangles on 6 and 7 points. Partially based on the Kepler triangle.

For 8 points, 24 right triangles are possible with a regular octagon. Dropping a point yields only 15 triangles, so the above solution is better.

The regular decagon gives 40 right triangles.
The regular dodecagon gives 60 right triangles.