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6

Part of 2023 Ecuador NMO (OMEC)

Problems(1)

All possible lengths of sides in that triangle

Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P6 day 2

11/6/2024
Let DEDE the diameter of a circunference Γ\Gamma. Let B,CB, C on Γ\Gamma such that BCBC is perpendicular to DEDE, and let QQ the intersection of BCBC with DEDE. Let PP a point on segment BCBC such that BP=4PQBP=4PQ. Let AA the second intersection of PEPE with Γ\Gamma. If DE=2DE=2 and EQ=12EQ=\frac{1}{2}, find all possible values of the sides of triangle ABCABC.
geometrynational olympiad