MathDB

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Part of 2023 Oral Moscow Geometry Olympiad

Problems(2)

Trapezoid and bisection

Source: Oral Moscow geometry olympiad 2023 8-9.1

4/20/2023
In trapezoid ABCDABCD with bases AD,BCAD, BC, AD=2BCAD = 2BC and MM is midpoint of ABAB. Prove that line BDBD passes through the midpoint of segment CMCM.
geometry
Geo with angle 60 degrees

Source: Oral Moscow geometry olympiad 2023 10-11.1

4/20/2023
In triangle ABC ∠ABC=60o\angle ABC=60^{o} and OO is the center of the circumscribed circle. The bisector BLBL intersects the circumscribed circle at the point WW. Prove that OWOW is tangent to (BOL)(BOL)
geometry