A Lemma of Archimedes about a Bisected Segment

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Let AB be the diameter of a semicircle. Let CB and CD be tangents. If DE is perpendicular to AB and DE intersects AC at F then DF = FE.


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Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA



The statement of the theorem is in Archimedes' Book of Lemmas: Proposition 2.

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