We drew two long arcs with the same radius from opposite sides of the circle, making a line that passes through where the arcs intersected. This finds the perpendicular bisector of the undrawn line connecting the two points the arcs originated from.
We turned the paper a rough 90° and repeated the same process. The instance where the two perpendicular bisectors intersect was the centre of the circle.
Proof of how we found the centre of the circle
The perpendicular bisector of any chord in a circle would be its diameter if extended from one point of the circumference to the other. This is because a line connecting the centre of the circle to a chord is perpendicular to the chord it connects the centre to.
What we have done is find the perpendicular bisector of two chords and, since the diameters would intersect in the centre, hence have used this method to find it.
Finding the diameter and radius of the circle
Extending or limiting the line drawn by the arc intercepts to exactly at the circumference and measuring this line, we found that the diameter was approximately 10.25 cm and that the radius was approximately 5.125 cm.