In the given triangle $ABC$, we see that $P$ is the centroid of the triangle, as the medians (the red lines) of the triangle converge at point $P$. A median of a triangle is a line drawn from a vertex to the midpoint of the opposite side. This fact gives us a useful property: the centroid divides each median into two segments, where the segment connecting the centroid to the vertex is twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Key information:

• $AZ = 33$ (where $Z$ is the midpoint of side $BC$).
• We are to find $AP$ and $PZ$.

Centroid property:

Since $P$ divides $AZ$ into a 2:1 ratio: