Question 74
Let $ABC$ be a triangle, and let $X$, $Y$, $Z$ be points on $BC$, $CA$, $AB$, respectively. Suppose that $AX$, $BY$ and $CZ$ intersect in a point $P$. Prove that
$$
\frac{AP}{AX} + \frac{BP}{BY} + \frac{CP}{CZ} = 2.
$$
$$
\frac{AP}{AX} + \frac{BP}{BY} + \frac{CP}{CZ} = 2.
$$