Difference between revisions of "Talk:Incenter"
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Minor point: can anyone give a quick argument that the angle bisectors actually have an intersection point? (This is slightly non-trivial -- one must decide if angle bisectors are rays or lines first.) --[[User:JBL|JBL]] 11:20, 7 September 2006 (EDT) | Minor point: can anyone give a quick argument that the angle bisectors actually have an intersection point? (This is slightly non-trivial -- one must decide if angle bisectors are rays or lines first.) --[[User:JBL|JBL]] 11:20, 7 September 2006 (EDT) | ||
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| + | I think that the section "Proof of Existance" does that. However, it assumes that the locus of points equidistant from the two lines is the angle bisectors, and also that any two given angle bisectors intersect. But it is fairly easy to see that if we assume that two of them are parallel, then we have a degenerate triangle. (We can also say that they intersect at the point of infinity, which is then the circumcenter of the triangle, which is true in the projective plane.) —[[User:Boy Soprano II|Boy Soprano II]] 17:05, 7 September 2006 (EDT) | ||
Revision as of 17:05, 7 September 2006
Minor point: can anyone give a quick argument that the angle bisectors actually have an intersection point? (This is slightly non-trivial -- one must decide if angle bisectors are rays or lines first.) --JBL 11:20, 7 September 2006 (EDT)
I think that the section "Proof of Existance" does that. However, it assumes that the locus of points equidistant from the two lines is the angle bisectors, and also that any two given angle bisectors intersect. But it is fairly easy to see that if we assume that two of them are parallel, then we have a degenerate triangle. (We can also say that they intersect at the point of infinity, which is then the circumcenter of the triangle, which is true in the projective plane.) —Boy Soprano II 17:05, 7 September 2006 (EDT)
