3. As shown in Figure $9, A B$ is the diameter of a semicircle, and $C$ is a point on the semicircular arc. One side $D G$ of the square $D E F G$ lies on the diameter $A B$, 
and the other side $D E$ passes through the incenter $I$ of $\triangle A B C$, with point 
$E$ on the semicircular arc. If the area of the square $D E F G$ is 
100, find the area of $\triangle A B C$.
(Given: $A D=\frac{b+c-a}{2}, B D=\frac{c+a-b}{2}$. From $D E^{2}$ $=A D \cdot D B$, we get $100=\frac{b+c-a}{2} \cdot \frac{c+a-b}{2}=\frac{a b}{2}$, hence $\left.S_{\triangle B B C}=100.\right)$