A Lemma of Archimedes about a Bisected Segment

DF

≈

0.49

FE

≈

0.49

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.

Details

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

External Links

Circle Tangent Line (Wolfram MathWorld)

Perpendicular (Wolfram MathWorld)

Permanent Citation

Jay Warendorff, Antonio Gutierrez

"A Lemma of Archimedes about a Bisected Segment"
http://demonstrations.wolfram.com/ALemmaOfArchimedesAboutABisectedSegment/
Wolfram Demonstrations Project
Published: March 7, 2011