MathDB

8.2

Part of 2022 Sharygin Geometry Olympiad

Problems(1)

right-angled trapezoid, angle bisection

Source: Sharygin Finals 2022 8.2

10/3/2022
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.
geometrytrapezoid