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Math: Geometry Problem 1112: Triangle, Excenters, Circumcircle, Circle, Hexagon, Area. Level: High School, College


The figure below shows a triangle ABC with the excenters E1, E2, and E3. Lines AE1, BE2, and CE3 meet circumcircle O at A1, B1, and C1, respectively. If S1, S2, and S3 are the areas of triangle E1E2E3, hexagon AC1BA1CC1, and triangle A1B1C1, respectively, prove that S1 = 2.S2 = 4.S3.

Geometry Problem 1112 Triangle, Excenters, Circumcircle, Circle, Hexagon, Area

See also: Kaleidoscope of Problem 1112 base on Poincare Disk Model.

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Last updated: Apr 24, 2015 by Antonio Gutierrez