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concyclic wanted, touchpoints of incircle

Source: 2023 China South East Mathematical Olympiad Grade 11 P5 CSMO

April 6, 2024
geometryConcyclicincircle

Problem Statement

As shown in the figure, in △ABC\vartriangle ABC, AB>ACAB>AC, the inscribed circle II is tangent to the sides BCBC, CACA, ABAB at points DD, EE, FF respectively, and the straight lines BCBC and EFEF intersect at point KK, DG⊥EFDG \perp EF at point GG, ray IGIG intersects the circumscribed circle of △ABC\vartriangle ABC at point HH. Prove that points HH, GG, DD, KK lie on a circle. https://cdn.artofproblemsolving.com/attachments/5/e/804fb919e9c2f9cf612099e44bad9c75699b2e.png
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