MathNet 2014 Question 93

Let $ABC$ be a triangle with sides $AB=6$, $BC=10$, and $CA=8$. Let $M$ and $N$ be the midpoints of $BA$ and $BC$, respectively. Choose the point $Y$ on ray $CM$ so that the circumcircle of triangle $AMY$ is tangent to $AN$. Find the area of triangle $NAY$.

Supplemental exact coordinate figure.