---
tag: HYVFPWS9ER
kind: concept
name: Cospherical points
msc: [51M04, 51M05]
sources:
  - url: https://en.wikipedia.org/wiki/Concyclic_points
---

## Summary

A set of points is cospherical if all of its points lie on one [[sphere|P9CM4GQ2T0]].
In the plane this is the same as being [[concyclic|049DCJZ448]].
Four points of space that do not lie in one plane are always cospherical, which gives every tetrahedron a circumscribed sphere.

## Explanations

### L1 human

Points are cospherical when one ball can be chosen whose surface passes through all of them.
The eight corners of a cube are cospherical: they all lie at the same distance from the centre of the cube.
Three distinct points on one straight line are never cospherical in the plane, since no circle meets a line in three points.