n points marked 1, 2, 3, ... n are evenly spaced around the circumference of a circle.

3 of the points are picked at random.

What is the probability that

(a) the points are the vertices of a right-angled triangle?

(b) the points are the vertices of an isosceles (including equilateral) triangle?

Answer (a) and (b) for n = 3, 4, 5, 6, 7

Bonus question (parts of this are quite tricky!)

Find general formulae that give these probabilities in terms of n, the number of points on the circumference. Explain how you know they are correct.