Is there exist postive integer $a,b,c,x,y,p,q$,such $(a,b,c),(x,y,a),(p,q,b)$ are a Pythagorean triple?

I.e $$\begin{cases} a^2+b^2=c^2\\ x^2+y^2=a^2\\ p^2+q^2=b^2 \end{cases}$$ have postive integers solution?

Do there exist postive integers $a,b,c,x,y,p,q$ such $(a,b,c)$, $(x,y,a)$, $(p,q,b)$ are all Pythagorean triples? That is, does the system $$\begin{cases} a^2+b^2=c^2\\ x^2+y^2=a^2\\ p^2+q^2=b^2 \end{cases}$$ have a postive integer solution?