I found this problem that I wrote 7 years ago. I originally solved it in a silly way, and was surprised by how magically the numbers worked out. Then I solved it in the intended obvious way and realized I was being silly. Also, I think the answer extraction is cute: it looks bad but it turns out to be decent.

In rectangle $ABCD$ with $AD=10$, let $E$, $F$ be the midpoints of $AB$, $CD$. Point P on segment $EF$ is such that $AP=6$ and $CP=8$. Find the area of $APC$.