Answer :

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 + y2 + 2by + b2 + z2 = x2 + y2 + z2


b(2y-b) = 0


as b ≠ 0.


y= b/2


CD = 0D



Squaring both sides,


=


x2 + y2 + 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).


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