Let A (x, y, z ) be a point in x y - 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).…

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