Consider the island of Great Britain. Imagine choosing 3 points on the coast, and connecting those points to make a triangle. I think there would be an infinite number of possible triangles. Would that still be the case if we added the condition that the sides of the triangle may not cross the coastline?
And is it possible to create even one equilateral triangle that doesn’t cross the coastline?
I have no clue how to approach as a general case.