How do you find the center of a circle with a pencil and a book? Given a circle on a paper, and a pencil and a book. Can you find the center of the circle with the pencil and the book?
Let the corner of the book just touch the circle's edge. You can draw two perpendicular lines along book's edge which intersect with the circle at two different points. Connect the two points and it's a diameter. 

Repeat this and get another diameter. The intersect of these two diameters is the center of the circle.
Hang the circle by its top edge on a wall close to a door or corner, draw a line straight down using the book's edge parallel to the door/corner edge. Rotate the circle f.ex 90 deg., draw a new line and you have the center and radius. This technique can also find the center of more complicated shapes. Gravity is the keyword here.