Compute the variance of the random variable X measuring the distance between P1 and P2

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Can anyone help me with this?

Consider the circle $C = \{f(x,y)\in\mathbb{R^2}: x^2 + y^2 = r^2\}$ and a point P2\in\mathbb{C}. A point P2\in\mathbb{C} is randomly chosen.

Compute the variance of the random variable X measuring the distance between P1 and P2.

The average between two points is 2rsin(θ/2) where θ is in [0,π]. But how can a find the pdf?