Question 40
Let $ABCD$ be a unit square. A circle with radius $\frac{32}{49}$ passes through point $D$ and is tangent to side $AB$ at point $E$. Then $DE=\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100m+n$.