Three Points Describe a Circle

From ProofWiki
Jump to: navigation, search

Theorem

Let $A$, $B$ and $C$ be points which are not collinear.

Then there exists exactly one circle whose circumference passes through all $3$ points $A$, $B$ and $C$.


Proof

As $A$, $B$ and $C$ are not collinear, the triangle $ABC$ can be constructed by forming the lines $AB$, $BC$ and $CA$.

The result follows from Circumscribing Circle about Triangle.

$\blacksquare$


Sources