Talk:Nine-point circle
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Took this out because it's wrong:
-:The excircle, by definition, is tangential to the midpoint of its side of the triangle, implying tangency to the nine point circle.
- , and is another way of stating tangency to the midpoints of the three sides
The excircle isn't tangent to the middle of a side unless the triangle is isosceles. Ditto the incircle and the nine-point circle. The nine-point circle in the picture isn't tangent to any side, it passes through the middles of them. The excircle and incircle are tangent to all three sides (extended for the excircles); the excircle's tangent point on the side it's on and the incircle's are on opposite sides of the middle. -phma
I plan on doing some reading on this. Should we / do we have a page on geometry of the circle or geometry of the triangle to give an overview of all these lines & things? -- Tarquin 20:32 Dec 24, 2002 (UTC)
- I surely vote for yes, but we have a lot of work to do then, and specially with both terms, right? Best regards. --XJamRastafire 04:12 Dec 25, 2002 (UTC)
Tarquin I've seen many times nine points 1,2,3,4,5,6,7,8,9 marked with E,F,G... or with other letters. I guess the latter is a better designation, since we usually mark points in geometry with capitalized letters. Perhaps N1, N2, N3, ... would also be fine? What do you think? Should I better correct the graph on enclosed picture? I still have to make the graph, describing Feuerbach's theorem alone. --XJamRastafire 02:37 Jan 2, 2003 (UTC)
- Yes, letters are more usual in geometry. It might be an idea to omit the "O" and the "=" signs, as that diagram appears quite cluttered at first. I can "decode" it but non-mathematicians might find it too complx.
- Could you also make a second diagram of the same triangle, but this time with the 9-pt circle, the incircle & one of the 3 excircles? -- Tarquin 10:39 Jan 2, 2003 (UTC)
- BTW, you should make the image a PNG, not a JPEG. You won't get the slight blurring around letters. -- Tarquin 22:38 Jan 4, 2003 (UTC)
- Here's the 2nd requested graph:
--XJamRastafire 11:17 Jan 10, 2003 (UTC)
The images keep getting better :-) What software do you use? I have one tiny request: the first picture of the 9 point circle doesn't need lines connecting F, D and E. AxelBoldt 21:50 Jan 10, 2003 (UTC)
- Done. I've already told you Axel. I use Maple V Release 4.00a. I have a questions too. How should we mark points in a triangle: clockwise or otherwise? I've marked them clockwise. I guess it doesn't matter as long as the longest side in a rightangled triangle is marked with C... --XJamRastafire 17:52 Jan 13, 2003 (UTC)
Thanks for restoring the article - you guys are so great!
[edit] Twelve-points circle?
This is given as an alternative name. What are the other three points of interest? -- Smjg 15:54, 15 September 2005 (UTC)
JTAI you could consider the other three points to be the points of tangency with the excircles. But if you're going to count these, shouldn't you count the point of tangency with the incircle, thereby making "thirteen-point circle" just as appropriate if not more?
OK, so there's the degenerate case of an equilateral triangle, in which this circle coincides with the incircle. But is this a valid reason to dismiss the view that there are thirteen points of interest? -- Smjg 01:08, 2 October 2006 (UTC)
