Question

Find the coordinates of the point which is equidistant from the points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0).

Answer 1

Let the required point be P(x, y, z). Then,

$P{A}^2=P{B}^2=P{C}^2=P{O}^2\iff P{A}^2-P{O}^2=0,P{B}^2-P{O}^2=0$ and $P{C}^2-P{O}^2=0$.