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Problem 337. Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points. Level: High School, College, SAT Prep.

The figure shows an isosceles trapezoid ABCD (AD // BC) inscribed in a circle. CE is the angle bisector of angle ACD. CE meet BD at F. A line L1 from F is parallel to BC and meets AC at G and CD at H. Prove that points D, E, G, and H are concyclic. .
 

Cyclic quadrilateral, trapezoid, angle bisector, concyclic

 

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