Question

Three points are chosen uniformly at random from the perimeter of circle. The probability that the triangle formed by these is acute can be expressed as a/b where a and b are co prime positive integers. What is the value of a+b?

Answer 1

if two of the points are a diameter apart, the triangle is a right triangle.

So, given that the first two points are on the same semi-circle, which they must be, then we want the probability that the third point is on the same semi-circle. If it is not, then the triangle will be acute, as all three arcs are less than 180 degrees.

So P = 1/2