Three Dimensional Geometry: JEE Main 2025 Mathematics question

Let $\mathbf{A}(x, y, z)$ be a point in $xy$-plane, which is equidistant from three points $(0, 3, 2)$, $(2, 0, 3)$ and $(0, 0, 1)$. Let $\mathbf{B} = (1, 4, -1)$ and $\mathbf{C} = (2, 0, -2)$. Then among the statements (S1): $\triangle ABC$ is an isosceles right angled triangle, and (S2): the area of $\triangle ABC$ is $\frac{9 \sqrt{2}}{2}$.