Polygons, Centroids & Circumcentres!

Geometry Level 3

$$X$$ is a polygon with $$n [\geq3]$$ sides. The centroid and the circumcentre of $$X$$ happens to be the same point. Read the following statements about $$X$$

$$[1]$$. If $$n=3$$, then $$X$$ is a regular polygon.

$$[2]$$ If $$n=4$$, then $$X$$ is not necessarily a regular polygon.

$$[3]$$. $$X$$ is a regular polygon whenever $$n\neq 4$$.

Which of these statements are correct?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.

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