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Part of 2020 Federal Competition For Advanced Students, P1

Problems(1)

segment of projections is half as sidelength, right triangle inscribed in right

Source: 2020 Austrian Federal Competition For Advanced Students, Part 1, p2

11/22/2020
Let ABCABC be a right triangle with a right angle in CC and a circumcenter UU. On the sides ACAC and BCBC, the points DD and EE lie in such a way that ∠EUD=90o\angle EUD = 90 ^o. Let FF and GG be the projection of DD and EE on ABAB, respectively. Prove that FGFG is half as long as ABAB.
(Walther Janous)
geometryequal segmentsright triangle