MathDB
Simple geometry

Source: 2021 MEMO T-5

September 5, 2021
geometrycircumcircleMEMO 2021memomenelaus theorem

Problem Statement

Let ADAD be the diameter of the circumcircle of an acute triangle ABCABC. The lines through DD parallel to ABAB and ACAC meet lines ACAC and ABAB in points EE and FF, respectively. Lines EFEF and BCBC meet at GG. Prove that ADAD and DGDG are perpendicular.
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