Question 88
Let $A B C$ be an acute triangle. Construct a triangle $P Q R$ such that $A B=2 P Q$, $B C=2 Q R$, $C A=2 R P$, and the lines $P Q$, $Q R$, and $R P$ pass through the points $A$, $B$, and $C$, respectively. (All six points $A, B, C, P, Q$, and $R$ are distinct.)