Junior Macedonian Mathematical Olympiad

A triangle $△ABC$ is given together with a segment $PQ$ of length $t$ on the segment $BC$, so that $P$ is between $B$ and $Q$ and $Q$ is between $P$ and $C$. We draw parallel lines from the point $P$ to $AB$ and $AC$ which intersect $AC$ and $AB$ in $P_1$ and $P_2$, respectively. We draw parallel lines from the point $Q$ to $AB$ and $AC$ which intersect $AC$ and $AB$ in $Q_1$ and $Q_2$, respectively. Prove that the sum of the areas of $PQ{Q}_1{P}_1$ and $PQ{Q}_2{P}_2$ doesn't depend on the position of $PQ$ on $BC$.