Geometry Tutorial #7 -Assorted Configurations (Theory)

#IMO​ #Geometry #MathOlympiad​ In this video we discuss the fourth chapter from EGMO book "Assorted Configurations". We study many common configurations that appear in many Olympiad geometry problems including (Simson's line Bisection, Duality of Orthocenters and Excenters, The Diameter of the Incircle, Midpoint of Altitudes, An Incircle Concurrency, Isogonal and Isotomic Conjugates, Symmedians, Circles Inscribed in Segments, Curvilinear Incircle Chord, and Mixtilinear Incircles). 00:00 Intro 2:23 Lemmas' Revision 4:52 Simson's line Bisection 22:11 Duality of Orthocenters and Excenters 27:27 The Diameter of the Incircle 37:04 Midpoint of Altitudes 41:35 An Incircle Concurrency 49:57 Isogonal and Isotomic Conjugates 59:49 Symmedians 01:38:12 Circles Inscribed in Segments 01:45:22 Curvilinear Incircle Chord 01:56:13 Mixtilinear Incircles 02:10:03 Summary Thanks to Arc for desigining the thumbnail. Inequalities playlist: https://youtube.com/playlist?list=PL1qInO9wTp3mgEn4_X2niePNxrX26OJBl&si=ELV8IYRYz5cyq0sG IMO Past Problems: https://youtube.com/playlist?list=PL1qInO9wTp3kBq7mFRtDauNbuQnddGd6H Functional Equations playlist: https://youtube.com/playlist?list=PL1qInO9wTp3lh0uGN9W6JufoBk7g0BDCL Geometry playlist: https://youtube.com/playlist?list=PL1qInO9wTp3lG6O06huPmQjR1kpeLDI76&si=DBuTjkYVTqTaMLIM Shorts: https://youtube.com/playlist?list=PL1qInO9wTp3m388GGbyWbw85LZRhn3dQw __________________________________________________________________________________________ I upload videos concerning math Olympiad contests to help students preparing for math Olympiad and all people who share the love for some interesting math problems. Don't forget to subscribe to the channel! __________________________________________________________________________________________ Email me your thoughts! ([email protected]) Discord server: https://discord.gg/RcP9eX9yg2 Donate: https://www.paypal.com/paypalme/hommeida?locale.x=en_US