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.
A. 6
B. 7
C. 8
D. 9
E. 10

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

1. 2026 AMC 8 官方解析

将等边三角形三边等分

$a, b, c$ 三边，任两边之和均小于6

$(1, 1, 1)$ $(1, 2, 2)$
$(1, 1, 2)$ $(1, 2, 3)$
$(1, 1, 3)$ $(2, 2, 2)$
$(1, 1, 4)$ $(2, 2, 3)$ 共8个

Answer

C. 8

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.