Problem

Source: Germany 2021, Problem 4

Tags: geometry, similar triangles, parallelogram, geometry proposed, lengths



Let $OFT$ and $NOT$ be two similar triangles (with the same orientation) and let $FANO$ be a parallelogram. Show that \[\vert OF\vert \cdot \vert ON\vert=\vert OA\vert \cdot \vert OT\vert.\]