Geometry Tutorial #5 -Lengths and Ratios (Theory)

#IMO​ #Geometry #MathOlympiad​ In this video we discuss the third chapter from EGMO book "Lengths and Ratios". We learn many ideas including (law of sines, Ratio lemma, Ceva's theorem, Menelaus's theorem, Centroid division, and finally homothety with nine-point circle). 00:00 Intro 1:11 Extended law of sines 8:23 Ratio lemma 13:39 Ratio of areas 19:45 Ceva's theorem 34:54 Menelaus's theorem 42:52 Centroid and medial triangle 49:13 Homothety 01:07:54 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