Can you construct the center of a given circle using a compass only. If the answer is yes, how?
I've had this question for a while, the only thing I was able to do is find a line containing the center. As a matter of fact, take $A,B$ two distinct arbitrary points of the circle. Draw the circle with radius $AB$ and center $A$, and let it cut the given circle in a point $C≠B$. Construct two circles, both with radius $BC$, one with center $C$ and one with center $B$. Intersect them in a point $D$. Thus $(AD)$ is the perpendicular bisector of $[BC]$, and therefore, contains the center of the given circle. This is what I got, and I don't know how to proceed.