2018 AIME I Problem 8

Let ABCDEF be an equiangular hexagon such that AB=6, BC=8, CD=10, and DE=12. Denote d the diameter of the largest circle that fits inside the hexagon. Find d^2.

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.