At first glance: n should BE the midpoint of the line segment be, and point D and point B should be on the same side of AC and its extension line, otherwise the conclusion will not hold. But it has not been proved. It doesn't seem to be a geometry problem in senior one. It's a little difficult.

Prove:

1, first prove that two triangles ACD and BCE are congruent-> ad = be;

2. It is proved that two small triangles AMC and BNC are congruent -> cm = CN, ∠ ACM = ∠ BCN-> ∠ MCN = 60 degrees;

Conclusion: Triangle CMN is an equilateral triangle.