A sphere of constant radius passes through the origin and meets the axis at and

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

A sphere of constant radius

k

passes through the origin and meets the axis at

A, B

and

C

. Prove that the centroid of triangle

ABC

lies on the sphere

9(x^2 + y^2 + z^2) = 4k^2