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A Lemma of Archimedes about a Bisected Segment


	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. Drag the red point to change the figure.


	Contributed by: Jay Warendorff After work by: Antonio Gutierrez

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

Circle Tangent Line (Wolfram MathWorld)

Perpendicular (Wolfram MathWorld)

"A Lemma of Archimedes about a Bisected Segment" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ALemmaOfArchimedesAboutABisectedSegment/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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