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You do not know how to find the centre of a circle. But can you find the centre of a equilateral triangle. If your answer is yes, then you make a concentric circle and a triangle. Let me explain.

First take a random point on the circle.

Now from that point draw two 60 degree angles. Then take the two points where those 60 degree angles meet the circumference. Now you have three points. Now join them. You get an equilateral triangle.Now take an angle and bisect it. Do the same with the other two angles. Are they not concurrent (meet at a same point?) Well now the place they meet is the centre of the triangle. And since the centre of the triangle and the circle is same, that is the centre.

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Q: Find the center of the circle without folding it?
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