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Geometry Problem 1162: Triangle, Congruence, Double Angle, Parallel Lines, Circle, Circumcenter. Level: School, College, Mathematics Education

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The figure below shows a triangle ABC with D and E on BC and F on AC so that BD = AF = FE = EC and angle BAD = 2 angle DAE = 2 angle EAC. Prove that (1) FD // AB, (2) B is the circumcenter of triangle AEF.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.

 

Geometry Problem 1162 Triangle, Congruence, Double Angle, Parallel Lines, Circle, Circumcenter

 


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