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

Subscribe to:
Post Comments (Atom)

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