Q. 14

# 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).

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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