MathDB

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Part of 2022 Costa Rica - Final Round

Problems(1)

BD _|_ CE , DEFO rhombus, ABC equilateral

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p1

3/26/2024
Let Γ\Gamma be a circle with center OO. Consider the points AA, BB, CC, DD, EE and FF in Γ\Gamma, with DD and EE in the (minor) arc BCBC and CC in the (minor) arc EFEF, such that DEFODEFO is a rhombus and △ABC\vartriangle ABC It is equilateral. Show that BD↔\overleftrightarrow{BD} and CE↔\overleftrightarrow{CE} are perpendicular.
geometryrhombusperpendicularperpendicularity