A random chord in a circle of radius r has a distance D from the center that is uniformly distributed between 0 and r. The length of the chord must be greater than the side of an equilateral triangle inscribed in the circle to satisfy the probability question. The side of an equilateral triangle inscribed in a circle of radius r is r√3/2.

1. Consider a circle of radius r . A chord is a line segment with both endpoints contained in the
circle. Assume that a random chord is a chord whose distance D from the center of the circle is
uniformly distributed between 0 and r . What is the probability that the length of a random chord
will be greater than the side of the equilateral triangle inscribed in that circle?