Equilateral+triangle+and+regular+9-gon

This is a contest problem from the [|AMC 12], a mathematical contest for 12th grade students in the United States.

//Given a nine-sided regular polygon, how many distinct equilateral triangles in the plane of the polygon have at least two vertices on the polygon?//

This GeoGebra applet can be used to visualize the problem. Can you find the solution?

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