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Draw two diameters of the circle and join the points where they meet the circumference.
No. Edges join vertices; or, put another way, edges meet at vertices.
If it is a polygon with an even number (>2) of vertices, join any two pairs of opposite vertices. These lines will meet in the centre. If it is a polygon with an odd number (>1) of vertices, join any two vertices to the midpoints of the opposite sides. These lines will meet in the centre.
When two lines meet to form an angle the lines are intersecting.
It is called a vertex