Please provide detail process, thanks

2- This problem illustrates how the interpretation of the word \"random\" may change probabilities. One wants to know the probability that a random chord in a circle of radius 1 has length less than x/g. (This number rep resents the side of an equilateral triangle inscribed in that circle-) It is however not clear how to choose a random chord- Here are two ways to do it. (a) (10 points) Two points are chosen randomly and independently of each other on the circle of radius 1 centered at the origin. (In usual coordinates a point on this circle is (cos t,sin t) for some t E [0, 2n), and choosing a point at random amoimts to choosing a value of t ac- cording to a uniform distribution on [0, 2n).) \"That is the probability that the distance between the two points is less than .5? (b) (10 points) A number r E (1,1) is chosen at random. \"That is the probability that the vertical chord in the circle of radius 1 centered at the origin and passing through (1', 0) has length less that f? (One may argue that a vertical chord is not really random, so in (b) one might want to consider two independent random choices: the distance from the center of the circle to the chord, and the direction of the chord. This however does not change the probability in (b).)