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TR-MO-R1 2016 Problem 1

    AB∥CDAB \parallel CD ve ∣AB∣>∣CD∣|AB| > |CD| olan bir ABCDABCD yamuğunda ACAC ve BDBD köşegenlerinin kesişim noktası EE dir. DECDEC üçgeninin çevrel çemberine EE noktasında teğet olan doğru [AB[AB ışınını FF noktasında kesiyor. ∣AF∣=9|AF| = 9, ∣AB∣=5|AB| = 5 ise ∣EF∣|EF| kaçtır?

    a) 5 b) 6 c) 7 d) 8 e) 9

    Official text Turkish Mathematical Olympiad, first round 2016 official paper, page 3. Quoted with source.

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