OE

Three different points A, B and C are equidistant from point O.
A) All four points can be in the same plane.
Consider a circle having center as O and A, B and C lie on the circumference. Hence,
Answer choice A is the Answer.
B) A, B and C points lie on the same plane.
Assume a cone where the vertex of the cone is O and A, B and C lie on the
circumference of the cone. So, this is also possible. Hence, Answer choice B is the
Answer.

C) A, B and C lie on a straight line.
As there is no point which is equidistant for three different points on a straight line,
hence Answer choice C is not the Answer.
D) A, B and C lie on a sphere with O as origin.
For a sphere, every point on the surface of the sphere is equidistant from the origin of
the sphere.
Hence, Answer choice D is the Answer.
Ans. (A, B, D)