Feuerbach’s theorem #SoME3

This is my video for #SoME3 In this video I will show a simple geometric proof of one of the most beautiful theorems of geometry - Feuerbach’s theorem. This theorem states that the Euler’s circle of an arbitrary triangle touches the inscribed and three escribed circles. This video includes many more different geometric facts, such as, for example, Miquel’s theorem or Archimedes’ lemma PDF (RU): PDF (EN): 00:00 Formulation of the theorem 00:54 Miquel’s Theorem 03:06 First consequence of Miquel’s Theorem 04:15 Second consequence of Miquel’s Theorem 07:59 Third consequence of Miquel’s Theorem 09:17 Archimedes’ lemma 11:05 External Archimedes’ lemma 12:52 Exercises 14:19 A few auxiliary theorems 16:42 Archimedes’ criteria 18:36 External Archimedes’ criteria 18:50 Feuerbach’s theorem 22:17 16 circles touch the Euler’s circle