Find the joint pdf of $X_1^2$ and $X_2^2$, where $(X_1, X_2)$ has a uniform distribution in the unit circle.

Question

I recently faced such a task:

If I understand correctly, then

$$f_{X_1, X_2}(s,t) = \begin{cases}\frac{1}{\pi}, & s^2+t^2 < 1 \\ 0 & \text{otherwise} \end{cases}$$ $$f_{|X_1|, |X_2|}(s,t) = \begin{cases}\frac{4}{\pi}, & 0<s<1; 0<t<\sqrt{1-s^2}\\ 0 &\text{otherwise}\end{cases}$$ But what to do next and how to find $f_{X_1^2, X_2^2}(s,t)?$ I will be grateful for any tips as I'm stuck with this exercise.