It is quite an interesting problem. Like the two-ladder one, seems simple, yet require brutal force to solve. And there's a trick here before set up the formulas.

Since the distance of each line of PQR is the same to ABC (2 units), then points P, Q, R are on the 角平分线 of angles A, B, C. That is the key to solve the problem. The rest is just to use brutal force to calculate. .......