Incenter, Orthocenter, Circumcenter, Centroid 삼각형 오심

The Euler line of a triangle is the line which passes through the 
orthocenter, circumcenter, and centroid of the triangle.  

       


The orthocenter is the intersection of the triangle's altitudes.

       


The circumcenter is the center of the circumscribed circle (the 
intersection of the perpendicular bisectors of the three sides).

       


The centroid is the intersection of the three medians of the triangle.

       


There's also the incenter, which is the intersection of the angle 
bisectors of the triangle.

       

-Doctor Pete,  The Math Forum

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NEWSGROUP DISCUSSIONS

For proofs involving the center of gravity and the circumcenter of a
triangle, see Eileen Steven's question sent to the newsgroup
geometry-pre-college, and Eileen Schoaff's answer:

  http://mathforum.org/kb/message.jspa?messageID=1077584   

  http://mathforum.org/kb/thread.jspa?forumID=128&threadID=351544   


For some properties of the orthocenter of a triangle, see Michael 
Keyton's posting to the newsgroup geometry-puzzles: 

  http://mathforum.org/kb/message.jspa?messageID=1084283   
  
  

Ask Dr. Mat