OBM 1991 Problem 2

$P$ is a point inside the triangle $ABC$ . The line through $P$ parallel to $AB$ meets $AC$ $A_0$ and $BC$ at $B_0$ . Similarly, the line through $P$ parallel to $CA$ meets $AB$ at $A_1$ and $BC$ at $C_1$ , and the line through P parallel to BC meets $AB$ at $B_2$ and $AC$ at $C_2$ . Find the point $P$ such that $A_0B_0 = A_1B_1 = A_2C_2$ .