Similar Triangle
An essential skill for intro-level synthetic geometry problems (AMC 8 / 10 level) and a must-have in more advanced analyses (AIME and beyond)
3. Advanced
2021 AIME I Problem 2 Problem 9
2021 AIME II Problem 2 Problem 10
2022 AIME II Problem 11 (the key is the auxiliary lines that takes full advantage of the angle bisectors and the midpoint)