Question about inscribed geometric shapes in circles

[cyoo1987]

When a geometric shape is inscribed inside a circle (such as a triangle, trapezoid, or square) does this mean that the center of this shape is also the center of the circle?

if this is true, can any line be drawn from the vertex (of the inscribed shape) to the center of the circle and be considered the radius of the circle?

[tim]

When a geometric shape is inscribed inside a circle (such as a triangle, trapezoid, or square) does this mean that the center of this shape is also the center of the circle?

if this is true, can any line be drawn from the vertex (of the inscribed shape) to the center of the circle and be considered the radius of the circle?

First, most geometric shapes do not have a well-defined center. For instance, a given triangle could have as many as four "centers" depending on which definition you use, ONE of which would also be the center of the circle (this center could even show up outside the triangle!)

for your second question, regardless of what shape you're using and what definition of center you're using, any vertex of the inscribed shape *by definition* lies on the circle, so any segment drawn from there to the center of the circle is *by definition* a radius..