Geometry Problem 1135: Intersecting Circles,
Secant, Parallel Line, 90 Degrees, Similar Triangles. Level: High School, SAT Prep,
Honors Geometry, College, Math Education

Circles O and Q intersect at A and B
(figure below) and E is a point on a secant CAD. EG and EF are
parallel to DB and CB, respectively. Angles BGJ and BFH are
equal to 90 degrees. Prove that (1) Triangles EGJ and HFE are
similar; (2) angle JEH = 90 degrees.