Ptolemy's TheoremĀ 

Ptolemy's theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral. It frequently shows up as an intermediate step in problems involving inscribed figures.


1991 AIME Problem 14

2004 AMC 10B Problem 24

2020 AIME I Problem 13

2021 AIME I Problem 11

2023 AIME I Problem 5