There is a contradiction in the question.
A circumscribed circle is the smallest circle that will contain the shape in question. For example, the circumcircle (circumscribing circle) of a triangle is the smallest one which will contain the triangle. However, the question refers to "within which the circle" which would imply an inscribed circle. This is the biggest circle that can be wholly enclosed within the shape in question.
The two are obviously not the same and the question needs to be clear as to which one of the two is intended.
When a polygon is within a circle and the circle touches each one of its corners it is referred to as circumscribed.
the center of a circumscribed circle is called the focus.
To circumscribed a circle about a triangle you use the angle. This is to get the right measurements.
A circumscribed polygon is a polygon all of whose vertices are on the circumference of a circle. The circle is called the circumscribing circle and the radius of the circle is the circumradius of the polygon.
A triangle has exactly one circumscribed circle.
No, only in certain, limited circumstances. Eg where a quadrilateral is (can be) circumscribed within a circle.
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.
Is equidistant from all points on the circle.
rectangle
No.No.No.No.
no
He circumscribed the square with a circle