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Nice equality of segments

Source: Central American Olympiad 2003, Problem 2

May 23, 2007
geometry

Problem Statement

Let ABAB be a diameter of circle ω\omega. ℓ\ell is the tangent line to ω\omega at BB. Take two points CC, DD on ℓ\ell such that BB is between CC and DD. EE, FF are the intersections of ω\omega and ACAC, ADAD, respectively, and GG, HH are the intersections of ω\omega and CFCF, DEDE, respectively. Prove that AH=AGAH=AG.
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