Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the complete problem 982.
Saturday, February 15, 2014
Geometry Problem 982. Triangle, Excenters, Excentral Triangle, Circumcenter, Area, Hexagon
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Let the intersection of circles O₁, O₂ and O₃ be O.
ReplyDeleteIt is easy to see that O is the orthocenter of E₁E₂E₃ and O₁O₂O₃.
Thus E₁A, E₂B and E₃C intersect at O.
The rest follows from the result of Problem 981.
3 angle bisectors AE1, BE2 and CE3 concurs at incenter I
ReplyDeleteIn right triangle IAE2 , O2 is the midpoint of IE2 => circle O2 will pass through I
Similarly circle O1 and O3 will pass through incenter I
This problem will become problem 981 and S1=2S2=4S3