Online Geometry Problem 715: Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC with the altitudes AA', BB' and CC'. The measure of angle BAC is 59 degrees. L is a line through A' parallel to B'C'. L meets AB extended and AC at D and E, respectively. B'C' and CB meet at F. The circumcircle of triangle DEF meets BC at H. Find the measure of angle B'HC'.