The Book of Lemmas: Proposition 12
If AB is the diameter of a semicircle, CD and CE are tangents to this semicircle from any point C, and AE and BD intersect at point F, then CF is perpendicular to AB.
Click and drag on the plot below to add point C to this diagram. After you plot C, the tangents CD and CE as well as the segments AE and BD are displayed, allowing you to observe whether CF is actually perpendicular to AB. Click the button to switch the points D and E and see that the lemma still holds.
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