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Two points are chosen randomly inside a circle (and even on the circumference) with radius $r$ What is the probability density function of the distance between the points? I would be very grateful.

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  • $\begingroup$ Hi! Rather than treat this as a homework solving site, perhaps you could relate what you've tried so far, and how that's worked out. $\endgroup$ – Brian Tung Apr 14 '15 at 3:22
  • $\begingroup$ Actually this is not a homework. I solved this by simulation (that was the homework). I just wanted some advices to proceed because i have not idea. i've tried : let two points inside the circle $p_1$ and $p_2$ i fixed $p_1$ and tried to calculate the cumulative distribution of the distance between the points $F(d)=P(D\leq d)=\frac{area(circle with center p_1 and radius d)}{Total area}$ and derivate $F(d)$ to obtain the density $f(d)$ i can't figure out how to obtain $F(d)$ without fixing $p_1$ $\endgroup$ – Marcos Fabian C Apr 14 '15 at 3:45

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