Let the points are $A(2,0,3), B(0,3,2)$ and $D(0,0,1) .$
We know that $Z$ -coordinate of every point an $x y$ -plane is zero so let $p(x, y, 0)$ be a point on $x y$ -plane such that $P A=P B=P C$.
Now, $P A=P B$
$\Rightarrow P A^{2}=P B^{2}$
$\Rightarrow (x-2)^{2}+(y-0)^{2}+(0-3)^{2}=(x-0)^{2}+(y-3)^{2} +(0-2)$
$\Rightarrow \, 4 x-6 y=0 \Rightarrow 2 x-3 y=0$ ...(i)
and, $P B=P C$
$\Rightarrow \, P B^{2}=P C^{2}$
$\Rightarrow (x-0)^{2}+(y-3)^{2}+(0-2)^{2}=(x-0)^{2}+(y-0)^{2}$
$+(0-1)^{2}$
$\Rightarrow \,-6 y+12=0$
$\Rightarrow \, y=2$ ...(ii)
Putting $y=2$ in Eq. (i), we get $x=3$ Hence, the required point is $(3,2,0)$.