Geometry Problem 931: Square, Circle, Semicircle, Diameter, Triangle, Angle, Metric Relations. Level: High School, SAT Prep, College, Mathematics Education

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In the square ABCD (see the figure below), let E be a point on the semicircle of diameter AD such that angle EBC = angle BAE + 45 degrees. If AE = 3, find BE.

Infographic Geometry Problem 931: Square, Circle, Semicircle, Diameter, Triangle, Angle, Metric Relations

Problem 931
Square ABCD stands firm,
E on semicircle sits poised,
Find BE's true length.