(a) A regular nonagon (9-sided polygon) is inscribed in a circle as shown below. Three of the 9 vertices are selected at random, and the triangle formed by those three points is drawn. What is the probability that the center of the circle lies inside the triangle? (A successful selection of 3 such points is shown below.)

(b) Generalize part (a): A regular -sided polygon is inscribed in a circle. Three of the vertices are selected at random, and the triangle formed by those three points is drawn. What is the probability (in terms of ) that the center of the circle lies inside the triangle?

Mr.Owl
Nov 13, 2017