Let X and Y be uniformly distributed on a unit disk such that

$x^2 + y^2 + 2 \leq 1$

Let $R = \sqrt{X^2 + Y^2}$. Find the CDF and PDF of $R$.

I start by writing

$P(X^2 + Y^2 \leq -1)$,

but this seems invalid. Two non-negative numbers cannot add to be less than -1. This is where I'm stuck.

Let X and Y be uniformly distributed on a unit disk such that

$x^2 + y^2 \leq 1$

Let $R = \sqrt{X^2 + Y^2}$. What are the CDF and PDF of $R$?

I know that the area of the unit disk is

$A = \pi r^2 = \pi 1^2 = \pi$

Thus, I think that the joint PDF of $X$ and $Y$ is the following, but I am not sure about this:

$f_{X, Y}(x, y) = \frac{1}{\pi}, \ \ \ x^2 + y^2 \leq 1$

I know that

$P(R \leq r) = P(\sqrt{X^2 + Y^2} \leq r)$.

This is where I'm stuck.