The general point on xy plane is D(x, y, 0). Consider this point is equidistant to the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).

∴ AD = BD

Squaring both sides,

=

X² – 4x +4 + y² + 9 = X² + y² -6y + 9 + 4

-4x = -6y ….(1)

Also, AD = CD

Squaring both sides,

=

X² – 4x +4 + y² + 9 = X² + y² +1

-4x = -12 ….(2)

Simultaneously solving equation (1) and (2) we get

X = 3, y = 2.

The point which is equidistant to the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1) is (3, 2, 0).