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Two similar triangles and a parallelogram called FANO

Source: Germany 2021, Problem 4

June 16, 2021
geometrysimilar trianglesparallelogramgeometry proposedlengths

Problem Statement

Let OFTOFT and NOTNOT be two similar triangles (with the same orientation) and let FANOFANO be a parallelogram. Show that ∣OF∣⋅∣ON∣=∣OA∣⋅∣OT∣.\vert OF\vert \cdot \vert ON\vert=\vert OA\vert \cdot \vert OT\vert.
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