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2020 Macedonian Junior BMO TST- P4

Source: 2020 Junior Macedonian Mathematical Olympiad

September 7, 2020
nicegeometrycollinearityjmmo2020circumcircleparallelogram

Problem Statement

Let ABCABC be an isosceles triangle with base ACAC. Points DD and EE are chosen on the sides ACAC and BCBC, respectively, such that CD=DECD = DE. Let H,J,H, J, and KK be the midpoints of DE,AE,DE, AE, and BDBD, respectively. The circumcircle of triangle DHKDHK intersects ADAD at point FF, whereas the circumcircle of triangle HEJHEJ intersects BEBE at GG. The line through KK parallel to ACAC intersects ABAB at II. Let IH∩GF=IH \cap GF = {MM}. Prove that J,M,J, M, and KK are collinear points.
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