MathNet 2024-part-06 — 165 problems (EN–VI) Question 40

In triangle $ABC$, points $M$ and $N$ are the midpoints of $AB$ and $AC$, respectively, and points $P$ and $Q$ trisect $BC$. Given that $A$, $M$, $N$, $P$, and $Q$ lie on a circle and $BC = 1$, compute the area of triangle $ABC$.