Not necessarily. If it is a semicircle - a circle bounded by an arc and the diameter of the original circle, it has two vertices - at the end of the diameter.
However, a half circle need not have a side that is a straight line. It can be like the yin-yang symbol (see link). The half circle here has no vertex.
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The shape that has no vertices and is round is a circle. The circle is the only shape that does not have vertices.
Zero vertices
None but it's possible to construct shapes within a circle that have vertices.
Inscribed
Circle or sphere.