Q: Is the vertex of a secant-tangent angle a point on a circle?

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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.

no never

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

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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.

no never

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.

No. A full angle is a segment of a line which goes to a vertex and returns along the same path. Any point on the line segment, other than the vertex, will trace out a circle but the angle itself is NOT a circle.

the vertex of the angle is the point

The vertex angle is connected to the vertex point

The vertex of an angle is the point at which the two rays that form the angle meet.opposite point

The point of an angle is its vertex

The sum of the angles around a vertex point in a plane will always be 360o. Picture a bicycle wheel with all its spokes radiating out from the hub. Now pick two spokes to form a vertex. Find the angle of your vertex, and then subtract it from 360o. As there are 360o in a circle, and your figure (the vertex) is a slice of the circle, its angle plus all the rest of the arc about the vertex will sum to 360o. If you've discovered the angle of your vertex, you cannot help but find the sum of the rest of the angles (if there are more than one) around your vertex.

The point about which an angle is measured