已知圆 $x^2+y^2-2x=0$的圆心为 $C$，直线 $\left\{\begin{array}{c}x=-1+\frac{\sqrt{2}}{2}t,\\ y=3-\frac{\sqrt{2}}{2}t\end{array}\right.$（ $t$为参数）与该圆相交于 $A$、 $B$两点，则 $\mathit{\Delta ABC}$的面积为___________.