Geometry Problems, Online Education

Problem 548: Triangle, Transversal, Complete Quadrilateral, Circumcircles, Circumcenters, Similarity, Concyclic Points. Level: High School, SAT Prep, College Geometry

The figure shows a triangle ABC with a transversal DEF (F on the extension of AC). O1, O2, O3, and O4 are the circumcenters of triangles ABC, BDE, ECF, and ADF, respectively. Prove that (1) the circumcircles of triangles ABC, BDE, ECF, and ADF meet at a point G, (2) Triangles ABC and O4O2O3. are similar, (3) O1, O2, O3, O4, and G are concyclic points (lie on a same circle). Post a comment or solution.
 

Triangle, Transversal, Circumcircle, Circumcenter, Concyclic
 

 

 

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Typography of problem 548

Typography and Sketch of Problem 548.

 

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