Isosceles triangles

Geometry Level pending

The \(ABC\) triangle is equilateral. The \(X, Y, Z\) points are respectively on the \(AB, BC, CD\) sides. We know that there are exactly \(n\) isosceles triangle from the \(AXZ, XBY, CZY, XYZ\) triangles. How many possible values are there for \(n\)?


This problem is from the "Kalmár László" Hungarian maths competition.
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