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perpendicular from interior point of a convex lies on a side

Source: 9th QEDMO p5 Seniors (21-22. 9. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
geometryconvex polygonconvexperpendicular

Problem Statement

Let PP be a convex polygon, so have all interior angles smaller than 180o180^o, and let XX be a point in the interior of PP. Prove that PP has a side [AB][AB] such that the perpendicular from XX to the line ABAB lies on the side [AB][AB].
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