geometry
posted by gorav .
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?

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 semicircle, which they must be, then we want the probability that the third point is on the same semicircle. If it is not, then the triangle will be acute, as all three arcs are less than 180 degrees.
So P = 1/2