The Book of Lemmas: Proposition 10
Let AB and AC be two tangents to a circle from point A, with AD cutting the circle between them. Let CE be the chord through C which is parallel to AD, and let BE intersect AD at point F. Then, if FG is drawn perpendicular to CE, the point G will bisect CE (and thus CG = EG).
Click and drag on the plot below to add point A and its tangents to the circle, AB and AC, to the diagram. Then, after clicking "Add point D", click and drag on the plot again to add point D and the segment AD to the diagram as well. Follow the rest of the steps given by the proposition by clicking "Add segments CE and BE", followed by "Add segment FG", and observe that the lengths of the segments CG and EG are always equal.
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