I began the same way as Beau with the drawing of a circle. Then i had drawn a chord from one side to the other. I then drew a line for the radius to one end of the chorde. The distance D is the line intersecting the chord at a 90 degree angle. Then you can use Pythagorean thm to find the distance L/2. Then to find the PDF of the whole chord, i just used the formula with the integral and used the parameters of D for the limits and fx(x) as 2 times the L.
