Question 57
The point $P$ lies inside the triangle $ABC$. A line is drawn through $P$ parallel to each side of the triangle. The lines divide $AB$ into three parts length $c$, $c'$, $c''$ (in that order), and $BC$ into three parts length $a$, $a'$, $a''$ (in that order), and $CA$ into three parts length $b$, $b'$, $b''$ (in that order). Show that $abc = a'b'c' = a''b''c''$.