Help with a mediocre geometry question

[AGeometryGuy]

Given a parallelogram ABCD, side AB is extended to a point P such that AB:BP =2:1 and side CD is extended to a point Q such that D is the midpoint of CQ. The line PQ meets the diagonal AC at Z and the sides BC and AD at X and Y , respectively.
(a) Find the ratio of the areas of triangles AZY and CZX.
(b) Find the ratio of the lengths PX and ZY.

It says to use similarity, but I see very few examples of similarity... Don't worry, you don't have to use it - just a tip from the question maker. I've no idea where to start...

 

[AGeometryGuy]

The only progression I've made is that XPB is similar to XCQ, and APZ is similar to CZQ. I just need to know how to begin to solve the problem...

 

[Dr.Peterson]

Start by making a more accurate drawing ... and check for a typo.