MathDB

2

Part of 2013 Korea Junior Math Olympiad

Problems(1)

tangent perpendicular to line, starting with a pentagon incribed in a circle

Source: KJMO 2013 p2

5/1/2019
A pentagon ABCDEABCDE is inscribed in a circle OO, and satis es AB=BC,AE=DEAB = BC , AE = DE. The circle that is tangent to DEDE at EE and passing AA hits ECEC at FF and BFBF at G(≠F)G (\ne F). Let DG∩O=H(≠D)DG\cap O = H (\ne D). Prove that the tangent to OO at EE is perpendicular to HAHA.
geometrypentagonperpendiculartangentcircles