For a triangle ABC with circumcircle c_{1} and internal angle bisector BD (see diagram) let EF
be perpendicular to BD, GH perpendicular bisector of AE, and JK perpendicular bisector of CF. Chord HL passes through E and chord KM passes through F, Prove that (1) Points M, E, F, and L are concyclic; (2) EF and HK are parallel.

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Geometry Problems

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Ten problems: 1411-1420

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Triangle

Circle

Triangle Centers

Circumcircle

Angle Bisector

Parallel lines

Perpendicular lines

Perpendicular
Bisector

Chord

Concyclic
Points

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