0 0 0 a 0 0 0 b 0 and 0 0 c are four distinct point What are the coordinates of the point whic...........

Mathematics (NDA) Coordinate Geometry

(0,0,0) , (a,0,0) , (0,b,0) and ( 0,0,c) are four distinct point . What are the coordinates of the point which is equidistant from the four points?

$\small \left ( \frac{a+b+c}{3} , \frac{a+b+c}{3},\frac{a+b+c}{3}\right )$

(a,b,c)

$\small \left ( \frac{a}{2},\frac{a}{2},\frac{a}{2} \right )$

$\small \small \left ( \frac{a}{3},\frac{a}{3},\frac{a}{3} \right )$

O(0,0,0)A(a,0,0),B(0,b,0) and C(0,0,c)
P(a/2,b/2,c/2) is equidistant from O, A,B and C.

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