Finding Center of Circle/Porism

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Porism to Finding Center of Circle

In the words of Euclid:

From this it is manifest that, if in a circle a straight line cut a straight line into two equal parts and at right angles, the centre of the circle is on the cutting straight line.

(The Elements: Book $\text{III}$: Proposition $1$ : Porism)


See Perpendicular Bisector of Chord Passes Through Center, where the proof has been extracted from the proof given by Euclid.