MathDB

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Part of 2017 IOM

Problems(1)

Simple parallelogram geo

Source: IOM 2017 #1

9/5/2017
Let ABCDABCD be a parallelogram in which angle at BB is obtuse and AD>ABAD>AB. Points KK and LL on ACAC such that ∠ADL=∠KBA\angle ADL=\angle KBA(the points A,K,C,LA, K, C, L are all different, with KK between AA and LL). The line BKBK intersects the circumcircle ω\omega of ABCABC at points BB and EE, and the line ELEL intersects ω\omega at points EE and FF. Prove that BF∣∣ACBF||AC.
parallelogramgeometryAngle Chase