Three Points Describe a Circle

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

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$