Go Geometry Problem Geometry Problem 1142: Cyclic Quadrilateral, Isogonal Lines, Circle, Center, Radius, Perpendicular Bisector, Circumcenter. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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The infographic below shows a cyclic quadrilateral ABCD. E is a point inside triangle CFG so that angle BAC = angle DAE (AC and AE are isogonal lines with respect to angle BAC). The perpendicular bisector of CE intersects AB and AD at O1 and O2, respectively. Circle of center O1 and radius O1C intersects AB at F. Circle of center O2 and radius O2C intersects AD at G. Prove that the circumcenter O3 of triangle EFG lies on AE.
 

Infographic Geometry problem 1142 Cyclic Quadrilateral, Isogonal Lines, Circle, Center, Radius, Perpendicular Bisector, Circumcenter


See also: Geometry problem 1142, Solution sent by Stan & Mihai Fulger

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Last updated: Jul 25, 2015 by Antonio Gutierrez.