SEAMO 2027 - Paper F - SET 02 - Self-study Question 10

In triangle $ABC$, $AC=2\sqrt{17}$, $BC=8$ and $AB=10$. Points $D,E,F$ are the midpoints of $BC,CA,AB$, respectively. Points $P,Q$ are the perpendicular projections of $A,D$ onto line $EF$. Find $PQ$.