Four Points on A Circle (Cyclic Quadrilaterals)

"A,B,C,D all lie on a circle..." an intimidating and confusing statement for beginners, a goldmine for experienced mathletes. Many useful tools exist to take advantage of concyclic points. POP (Power of a Point) and Ptolemy's just to name two. 


2019 AIME I Problem 13

2021 AIME I Problem 11

2021 AIME II Problem 14

2023 AIME II Problem 12

2024 AIME I Problem 5