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AC bisects BE, BC = DE, CD//BE, <BAC = <DAE, AB/BD=AE/ED

Source: China Northern MO 2012 p7 CNMO

October 28, 2022
geometrybisects segmentpentagon

Problem Statement

As shown in figure , in the pentagon ABCDEABCDE, BC=DEBC = DE, CD∥BECD \parallel BE, AB>AEAB>AE. If ∠BAC=∠DAE\angle BAC = \angle DAE and ABBD=AEED\frac{AB}{BD}=\frac{AE}{ED}. Prove that ACAC bisects the line segment BEBE. https://cdn.artofproblemsolving.com/attachments/3/2/5ce44f1e091786b865ae4319bda56c3ddbb8d7.png
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