2024 AIME I Problem 5

Rectangle ABCD has dimensions AB = 107 and BC = 16, and rectangle EFGH has dimensions EF = 184 and FG = 17. Points D, E, C, and F lie on line DF in that order, and A and H lie on opposite sides of line DF, as shown. Points A, D, H, and G lie on a common circle. Find CE.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.