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Source: PRMO Leg 2 P29

August 25, 2019
geometryPRMO

Problem Statement

Let ABCABC be an acute angled triangle with AB=15AB=15 and BC=8BC=8. Let DD be a point on ABAB such that BD=BCBD=BC. Consider points EE on ACAC such that ∠DEB=∠BEC\angle DEB=\angle BEC. If α\alpha denotes the product of all possible values of AEAE, find ⌊α⌋\lfloor \alpha \rfloor the integer part of α\alpha.
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