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Problem 642. Archimedes' Book of Lemmas: Proposition 3.
Level: High School, SAT Prep, College geometry.

Let C be any point on a semicircle of diameter AB, and let CD be perpendicular to AB. Take E on AB so that AD = DE. Take F on arc CB so that arc CF = arc AC. Prove BF = BE.
 

Archimedes Book of Lemmas: Semicircle, Tangent, Perpendicular 
 

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