VWO 2007 Problem 3

Let $ABCD$ be a square with side $10$ . Let $M$ and $N$ be the midpoints of $[AB]$ and $[BC]$ respectively. Three circles are drawn: one with midpoint $D$ and radius $|AD|$ , one with midpoint $M$ and radius $|AM|$ , and one with midpoint $N$ and radius $|BN|$ . The three circles intersect in the points $R, S$ and $T$ inside the square. Determine the area of $\triangle RST$ .