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angle bisector wanted, AD=CD=CB, AB // CD (2010 Romania District VII P4)

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May 19, 2020
geometryangle bisectorequal anglesequal segments

Problem Statement

We consider the quadrilateral ABCDABCD, with AD=CD=CBAD = CD = CB and AB∥CDAB \parallel CD. Points EE and FF belong to the segments CDCD and CBCB so that angles ∠ADE=∠AEF\angle ADE = \angle AEF. Prove that: a) 4CF≤CB4CF \le CB , b) if 4CF=CB4CF = CB, then AEAE is the bisector of the angle ∠DAF\angle DAF.
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