Geometry Problem 1559: Proving BC Bisects Segment DE

Challenging Geometry Puzzle: Problem 1559. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Problem 632: Triangle, Interior and Exterior Angle Bisectors, Midpoints, Collinear Points

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

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Problem 513: Triangle, Double Angle, Exterior Angle Bisector, Measure

Geometry Problem
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Level: High School, SAT Prep, College geometry

Problem 338. Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points

Proposed Problem
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Level: High School, SAT Prep, College geometry