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5 points and tangent(s)

Source: Italy National Olympiad 2020 P1

September 30, 2020
geometrycircumcircle

Problem Statement

Let ω\omega be a circle and let A,B,C,D,EA,B,C,D,E be five points on ω\omega in this order. Define F=BC∩DEF=BC\cap DE, such that the points FF and AA are on opposite sides, with regard to the line BEBE and the line AEAE is tangent to the circumcircle of the triangle BFEBFE. a) Prove that the lines ACAC and DEDE are parallel b) Prove that AE=CDAE=CD
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