Given: Points are A(3, 2, 2), B(-1, 4, 2), C(0, 5, 6), D(2, 1, 2)

To prove: given points lie on sphere whose centre is (1, 3, 4)

To find: radius of sphere

Let Center is O(1, 3, 4)

Since O is centre of sphere and A, B, C, D lie on a sphere

⇒ OA = OB = OC = OD = radius

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by,

Therefore,

The distance between O(1, 3, 4) and A(3, 2, 2) is OA,

= 3

Distance between O(1, 3, 4) and B(-1, 4, 2) is OB,

= 3

Distance between O(1, 3, 4) and C(0, 5, 6) is OC,

= 3

Distance between O(1, 3, 4) and D(2, 1, 2) is OD,

= 3

Clearly,

OA = OB = OC = OD = 3 units

Therefore, radius of sphere = 3 units and A, B, C, D lie on sphere having centre O