A Parallelogram Defined by the Centers of Four Circumcircles

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Let ABC be a triangle. Let the line DE be parallel to AC with D on AB and E on BC. Let the line GH be parallel to AB with H on AC and G on BC. Let F be the intersection of DE and GH. Let O, , , and be the circumcircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then is a parallelogram.

Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA



The statement of the theorem is in Problem 93. Similar Triangles, Circumcircles, Parallelogram.

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