The Geogebra applet below shows a rectangle and a circle. Using the rectangle and some basic tools, you can find the centre of the circle.
A solution
We know that the angle in a semicircle is 90 degrees. The converse is also true. Use the right angle of the rectangle to identify a diameter. Two diameters intersect at the centre. See below.
Note: This demonstration wasn't accurate. It was more of an exploration into the possible methods for finding the centre of the circle. With more tools, you can construct precise diagrams.
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