Unlock the Secrets of Incenter and Excenter with this Geometry Lemma скачать в хорошем качестве

Unlock the Secrets of Incenter and Excenter with this Geometry Lemma

Let ABC be a triangle with incenter I, line AI meets the circumcircle of △ABC again at L. We let I_A be the reflection of I over L. Then, we have two facts, first fact is (a) the points I, B, C and I_A lie on a circle with diameter II_A and center L. In particular, LI = LB = LC = LI_A. The second fact is (b) lines BI_A and CI_A bisect the exterior angles of △ABC. In other words, they are the exterior angle bisectors of ∠B and ∠C. Can you prove this lemma? Well, this is a useful lemma in Euclidean geometry, especially if you are solving Math Olympiad geometry problems and I want to point out a great book in learning it which is the ”Euclidean Geometry in Mathematical Olympiad” by Evan Chen, there is a link below to this book. 🔥Subscribe to 1Psi3Colour: https://www.youtube.com/c/1Psi3Colour... Video Chapters: 0:00 The Lemma 1:09 First fact 3:31 Second fact 4:51 Outro + Subscribe! ”Euclidean Geometry in Mathematical Olympiad” by Evan Chen: https://web.evanchen.cc/geombook.html 💥Check out these videos: The integral everyone should know:    • The MOST Influential Integral In ALL ...   A deceivingly easy Putnam problem!:    • Is This THE EASIEST Problem On THE HA...   👉Check out these playlists: Math Olympiad:    • Math Olympiad   Math puzzles:    • Math puzzles   College Math:    • College Math   This video is created using Manim: https://www.manim.community 👉Suggest a problem: https://forms.gle/hTibrUKz7QNyqoC48