no never
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An angle with its vertex on the center point of the circle.
This is the definition of an inscribed angle in geometry. An inscribed angle is formed by two chords in a circle that also share a common point called the vertex.
Yes.
If the vertex is at the centre of the circle then this forms a sector of the circle.If the two endpoints and the vertex form an angle in a segment, then the vertex can be at any point on the circle within the same segment and all angles so formed are equal.
the vertex of the angle is the point