Let $n\in$ \reftext{def:natural-numbers-2026a}{$\mathbb{N}$}, and let $A$, $B$, $C$ be points of \reftext{def:euclidean-space-rn-2026a}{Euclidean space} $\mathbb{R}^n$. Assume that the \reftext{def:dot-product-orthogonality-rn-2026a}{differences} $B-A$ and $C-A$ are \reftext{def:dot-product-orthogonality-rn-2026a}{orthogonal}, that is,

Then, with $d_E$ denoting the \reftext{def:euclidean-distance-rn-2026a}{Euclidean distance} on $\mathbb{R}^n$,

\textit{In the classical picture, $A$ is the vertex of the right angle of a right triangle, $d_E(A,B)$ and $d_E(A,C)$ are the lengths of the two legs, and $d_E(B,C)$ is the length of the hypotenuse.}