Hi Golland,

In my previous reply I said message #4. It's different now - seems messages are renumbered when a new one is inserted.
With respect to how many lines there are at a point; here is my conjecture:
Consider a deltoid with vertices at the midpoints of the medians.
Any point in the exterior of the deltoid has only one solution.
Any point on the boundary of the deltoid has two solutions; unless it is a vertex, then it has only one.
Any point in the interior has two solutions; unless it is on a median, then it has three.
What do you think of the conjecture?

Bractals