Points on a sphere

Geometry Level 2

Three points are chosen completely at random on the surface of a sphere.

What is the probability they all lie on the same plane?

50% 75% Insufficient information to determine 100% Some other number of % 25%

Denton Young by Denton Young , 47, USA

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2 solutions

Denton Young
Feb 15, 2017

ANY three points in space are coplanar, whether they are chosen on the surface of the given sphere or not.

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Pratyush Pandey
Feb 15, 2017

Join the arbitrarily picked 3 points with each other. You get a triangle (with vertices as the three chosen points). Now we know that triangle is a 2D figure, which is to say that it lies in a single plane. Hence, the triangle and all points on it are conplanar. Further we conclude that any three arbitrarily chosen points in 3D space are conplanar.

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