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two perpendiculars and a line of a parallelogram are concurrent, equal angles

Source: Greek National 2020 p2 (Archimedes)

February 23, 2020
geometryparallelogramequal anglesconcurrencyconcurrent

Problem Statement

Given a line segment ABAB and a point CC lies inside it such that AB=3⋅ACAB=3 \cdot AC . Construct a parallelogram ACDEACDE such that AC=DE=CE>ARAC=DE=CE>AR. Let ZZ be a point on ACAC such that ∠AEZ=∠ACE=ω\angle AEZ=\angle ACE =\omega. Prove that the line passing through point BB and perpendicular on side ECEC, and the line passing through point DD and perpendicular on side ABAB, intersect on point , let it be KK, lying on line EZEZ.
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