2026 AMC 8 Problem 25

In an equiangular hexagon, all interior angles measure 120^\circ. An example of such a hexagon with side lengths of 2, 3, 1, 3, 2, and 2 is shown below, inscribed in equilateral triangle ABC. Consider all equiangular hexagons with positive integer side lengths that can be inscribed in \triangle ABC, with all six vertices on the sides of the triangle. What is the total number of such hexagons? Hexagons that differ only by a rotation or a reflection are considered the same.

\textbf{(A)} 4 \qquad \textbf{(B)} 5 \qquad \textbf{(C)} 6 \qquad \textbf{(D)} 7 \qquad \textbf{(E)} 8

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