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Online Math: Geometry Problem 1213: Triangle, Circumcircle, Altitudes, Cyclic Quadrilateral, Congruence. Tiled background image: Intihuatana, Machu Picchu. Level: College, High School.

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The figure shows the circumcircle of a triangle ABC with the altitudes AD, BE, and CF. EF extended cuts arc AB at M. Lines BM and DF meet at N. Prove that (1) AFMN is a cyclic quadrilateral; (2) AM = AN.
This entry contributed by Peter Tran.
 

Geometry Problem 1213: Triangle, Circumcircle, Altitudes, Cyclic Quadrilateral, Congruence.
 
 

 

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Last updated: May 11, 2016