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assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed
A pentagon is a five sided geometrical figure; if the pentagon fits exactly inside some other geometrical figure (such as a circle) then it can be said to be inscribed in that figure.
The vertices of a pentagon are the five points where its sides meet. In a regular pentagon, these vertices are equidistant from the center and are evenly spaced around a circle. In general, the coordinates of the vertices can vary depending on the specific shape and size of the pentagon. For example, a regular pentagon inscribed in a unit circle has vertices at angles of (72^\circ) increments from a starting point.
Nothing particular. One of the properties of regular polygons - however many sides - is that it can have a circle inscribed in it.
The radius of a circle inscribed in a regular hexagon equals the length of one side of the hexagon.
I assume you mean a polygon inscribed in a circle. It is regular if all its sides and angles are equal.
If you know the length of the side of the (regular) hexagon to be = a the radius r of the inscribed circle is: r = a sqrt(3)/2
circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.
The circle has a smaller area than the polygon.
Inscribed Polygon
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