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Source: Canada Repechage 2022/7 CMOQR

March 19, 2022
geometryCanadarepechage

Problem Statement

Let ABCABC be a triangle with ∣AB∣<∣AC∣|AB| < |AC|, where ∣⋅∣| · | denotes length. Suppose D,E,FD, E, F are points on side BCBC such that DD is the foot of the perpendicular on BCBC from AA, AEAE is the angle bisector of ∠BAC\angle BAC, and FF is the midpoint of BCBC. Further suppose that ∠BAD=∠DAE=∠EAF=∠FAC\angle BAD = \angle DAE = \angle EAF = \angle FAC. Determine all possible values of ∠ABC\angle ABC.
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