Find the coordina

Consider, D(x,y,z) point equidistant from points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0).

∴ AD = 0D

Squaring both sides,

=

x² +2ax + a² + y² + z² = x² + y² + z²

a(2x-a) = 0

as a ≠ 0.

X = a/2

∴ BD = 0D

Squaring both sides,

=

x² + y^{2 +} 2by + b² + z² = x² + y² + z²

b(2y-b) = 0

as b ≠ 0.

y= b/2

∴ CD = 0D

Squaring both sides,

=

x² + y^{2 +} z² + 2cz + c² = x² + y² + z²

c(2z-c) = 0

as c ≠ 0.

z= c/2

Therefore, the pint D(a/2,b/2,c/2) is equidistant to points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0).