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Romania TST 2021 Day 1 P3

Source:

May 15, 2021
geometryRomanian TSTTSTcyclic quadrilateral

Problem Statement

The external bisectors of the angles of the convex quadrilateral ABCDABCD intersect each other in E,F,GE,F,G and HH such that A∈EH, B∈EF, C∈FG, D∈GHA\in EH, \ B\in EF, \ C\in FG, \ D\in GH. We know that the perpendiculars from EE to ABAB, from FF to BCBC and from GG to CDCD are concurrent. Prove that ABCDABCD is cyclic.
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