MathNet 2022-part-02 — 197 problems (EN–VI) Question 167

$ABCD$ is a parallelogram with $\angle B$ acute. A circle is tangent to $BC$, $CD$ and $DA$. The circle intersects $AC$ at $M$ and $N$, where $M$ is closer to $A$ than $N$. If $AM = 9$, $MN = 16$ and $NC = 2$, find the area of $ABCD$.