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Online Math: Geometry Problem 1227: Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral. Tiled background image: Intihuatana, Machu Picchu. Level: College, High School.

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D and E lie on BC of a triangle ABC such that AE bisects angle DAC (see the figure), The circumcircle of triangle ABD cuts AE at F and BF meets AC at P. DF and EP (extended) meet at R. Prove that (1) Points A, F, P, and R are concyclic; (2) Points A, D, E, and R are concyclic.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka. 
 

Geometry Problem 1227: Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral.
 
 

 

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Last updated: Jun 11, 2016