The evaluation of circularity based on the minimum circumscribed circle method is an important method suitable for the circle with the maximum material condition of a convex like a shaft. The minimum circumscribed circle is determined by a small number data points according to the criteria of the minimum circumscribed circle. This article points out the minimum circumscribed circle can be obtained only at vertices of convex hull. Based on three theorems developed, a strategy is proposed to identify the critical data points. The validated results show that the method gives an efficient approach to solve the circularity problems on the minimum circumscribed circle, especially when the number of data points is large.
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