MathDB
Isosceles and Concurrency

Source: Italy National Olympiad 2020 P4

September 30, 2020
geometrycircumcircle

Problem Statement

Let ABCABC be an acute-angled triangle with AB=ACAB=AC, let DD be the foot of perpendicular, of the point CC, to the line ABAB and the point MM is the midpoint of ACAC. Finally, the point EE is the second intersection of the line BCBC and the circumcircle of △CDM\triangle CDM. Prove that the lines AE,BMAE, BM and CDCD are concurrents if and only if CE=CMCE=CM.
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