Question 21
In the triangle $ABC$, $D$ is the midpoint of $AC$, $E$ is the midpoint of $BD$, and the lines $BA$ and $CE$ are tangent to the circumcircle of the triangle $ADE$ at $A$ and $E$ respectively. Suppose the circumradius of the triangle $AED$ is $\left(\dfrac{64}{7}\right)^{1/4}$. Find the area of the triangle $ABC$.