CMO 2019 Problem 2

Call a set of 3 positive integers $\{a,b,c\}$ a Pythagorean set if $a,b,c$ are the lengths of the 3 sides of a right-angled triangle. Prove that for any 2 Pythagorean sets $P,Q$ , there exists a positive integer $m\ge 2$ and Pythagorean sets $P_1,P_2,\ldots ,P_m$ such that $P=P_1, Q=P_m$ , and $\forall 1\le i\le m-1$ , $P_i\cap P_{i+1}\neq \emptyset$ .