Complex sentence: Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle, but every polygon has unique minimum bounding circle, which may be constructed by a linear time algorithm.
Split into simpler sentences: Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle. Yet any polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.