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right-angled trapezoid, angle bisection

Source: Sharygin Finals 2022 8.2

October 3, 2022
geometrytrapezoid

Problem Statement

Let ABCDABCD be a right-angled trapezoid and MM be the midpoint of its greater lateral side CDCD. Circumcircles ω1\omega_{1} and ω2\omega_{2} of triangles BCMBCM and AMDAMD meet for the second time at point EE. Let EDED meet ω1\omega_{1} at point FF, and FBFB meet ADAD at point GG. Prove that GMGM bisects angle BGDBGD.
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