Find the coordinates of a point equidistant from the four points O (0, 0, 0), A (l, 0, 0), B (0, m, 0) and C (0, 0, n).
Find the coordinates of a point equidistant from the four points O (0, 0, 0), A (l, 0, 0), B (0, m, 0) and C (0, 0, n).
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Let P (x, y, z) be the required point. Then OP = PA = PB = PC.
Now OP = PA ⇒OP2 = PA2 ⇒ x2 + y2 + z2 = (x – l)2 + (y – 0)2 + (z – 0)2 ⇒ x = i/2
Similarly, OP = PB ⇒ y =m/2 and OP = PC ⇒ z = n/2
Hence, the coordinate of the required point are (l/2,m/2,n/2)
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