gosh geometry... help plz?

Question

In parallelogram ABCD, AB>BC. Point P lies on diagonal AC so that P is equidistant from both AB and BC. SImilarly point Q lies on AC so that Q is equidistant from both CD and AD. If PQ = AC/4, find the ratio of AB:BC

Plz help, I'm stuck...

Answer 1

Triangles ABP and CBP are similar (identical angles).

AB / BC = AP / CP = (5/8 AC) / (3/8 AC) = 5/3

-