The circumstances of a circle are that it is a perfectly round shape and that its perimeter is better known as its circumference.
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A circle is a locus of all points which are at the same distance from some fixed point.
It is its radius that is the distance from the center of the circle to its circumference.
A curve. It may have a more specific name in some circumstances - eg a circle or a parabola.
No, only in certain, limited circumstances. Eg where a quadrilateral is (can be) circumscribed within a circle.
A circle graph, or pie chart is best used for showing parts of a whole.
The best tool to locate the center of a circle would be a compass. By placing the compass on the edge of the circle and drawing an arc, then repeating this process from another point on the circle, the intersection point of the arcs will give you the center of the circle.