Thales's theorem/Linear algebra/Fact

Let ${\displaystyle {}P}$ be a point in the Euclidean plane ${\displaystyle {}E}$, let ${\displaystyle {}K}$ be a circle with center ${\displaystyle {}P}$, and let ${\displaystyle {}G}$ be a line through ${\displaystyle {}P}$, intersecting the circle in the points ${\displaystyle {}A}$ and ${\displaystyle {}B}$.

Then for every point

${\displaystyle {}C\in K}$,

the triangle ${\displaystyle {}A,B,C}$ is a right triangle with the right angle at ${\displaystyle {}C}$.