Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 982.
Let the intersection of circles O₁, O₂ and O₃ be O. It 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 IIn right triangle IAE2 , O2 is the midpoint of IE2 => circle O2 will pass through ISimilarly circle O1 and O3 will pass through incenter IThis problem will become problem 981 and S1=2S2=4S3