IMO 2023 Problem 2: Full Solution with a Homothety

A tangent to one circle and a line through two points should not meet on the angle bisector by accident, yet in IMO 2023 Problem 2 they always do. This video experiments first, then shows two tempting approaches and exactly why they stall. It finds one right angle and a negative homothety that make the whole configuration fall into place. Problem: IMO 2023 Problem 2 (Shortlist G4) Official solution: https://www.imo-official.org/assets/d... Answer cross-checked against: evanchen.cc, imo-official.org Chapters: 0:00 The Problem 0:51 Experiments First 1:41 Tempting Dead Ends 2:38 Finding the Idea 3:41 The Proof 9:06 Why It Works 9:46 Takeaway The solution in this video is our own write-up and explanation; see the link above for the source. #IMO2023 #IMO2023Problem2 #IMOShortlist2023 ━━━━━━━━━━━━━━━ 🧮 Everyday Olympiad: one olympiad problem, solved step by step. 👉 Subscribe for more problems:    / @matholover   ✏️ Try it yourself first: pause after the problem statement and give it 10 minutes. 💬 Which problem should we solve next? Comment the competition and year!