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4CF<= CB, 4CF = CB => AE is bisector of <DAF, AD=DC=CB<AB, <ADE=<AEF

Source: 2011 Saudi Arabia Pre-TST February 1.3 https://artofproblemsolving.com/community/c2745403_2011_

January 1, 2022
geometric inequalitygeometryangle bisector

Problem Statement

The quadrilateral ABCDABCD has AD=DC=CB<ABAD = DC = CB < AB and AB∥CDAB \parallel CD. Points EE and FF lie on the sides CDCD and BCBC such that ∠ADE=∠AEF\angle ADE = \angle AEF. Prove that: (a) 4CF≤CB4CF \le CB. (b) If 4CF=CB4CF = CB, then AEAE is the angle bisector of ∠DAF\angle DAF.
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