Let $A,B,C,D$ be points on a circle, and let the lines $\overline{AC}$ and $\overline{BD}$ intersect at the point K. Prove that $|KA| \cdot |KC| = |KB| \cdot |KD|$.
Apparently the proof can be done using vectors but I don't know where to start.
All help is appreciated. Thank you.
hint: $\vec{KA} \cdot \vec{KC} =|KA|\cdot |KC| \cos {\theta}=-|KA|\cdot |KC|$
$|KA| \cdot |KC| = |KB| \cdot |KD| \iff \vec{KA} \cdot \vec{KC}=\vec{KB} \cdot \vec{KD}$
$\vec{KA}=\vec{KO}-\vec{AO},|AO|=|BO|=...$