Let \(A(x, y, z)\) be a point in \(xy-\)plane, which is equidistant from three points \((0, 3, 2), (2, 0, 3)\) and \((0,…

Let \(A(x, y, z)\) be a point in \(xy-\)plane, which is equidistant from three points \((0, 3, 2), (2, 0, 3)\) and \((0, 0, 1).\)
Let \(B = (1, 4, –1)\) and \(C = (2, 0, –2).\) Then among the statements

\((S1) : \Delta ABC\) is an isosceles right angled triangle and
\((S2) :\) the area of \(∆\mathrm{ABC}\text{ is }\frac{9\sqrt{2}}{2}.\)

[JEE Main 2025, 28 Jan (Shift 1)]