Find the point in XY-plane which is equidistant from three points A(2,0,3), B(0,3,2) and C(0,0,1)

Hello student,
Since we are required to find out the point in the xy-plane, hence the z-coordinate would be zero.
Let the required point be P(x, y, 0).
Then AP = BP = CP (Since it is equidistant from A, B and C.
Hence, AP² = BP² = CP²
AP² = CP²
This means, (x-2)² + (y-0)² + (0-3)² = (x-0)² + (y-0)² + (0-1)²
x² + 4 – 4x + y² + 9 = x² + y² + 1
We get x = 3.
BP² = CP²
This means, (x-0)² + (y-3)² + (0-2)² = (x-0)² + (y-0)² + (0-1)²
x² + y² + 9 – 6y + 4 = x² + y² + 1
We get y = 2.
Hence, the required point is P(3,2 ,0).