Right triangle altitude theorem/Linear algebra/Fact/Proof/Exercise

Let $A,B,C$ be a right triangle, with the right angle located at $C$. Let $h$ be the altitude through $C$, and let $D$ denote the foot of this altitude through the linen given by $A$ and $B$. Show that

$d(C,D{)}^2=d(A,D)\cdot d(B,D)$

holds.

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