Mathematics Question from JEE Main 2025 · 28 January, Shift 1

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