Talk:Orthocentric system
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Proof of a common nine point circle
[edit]If four points form an orthocentric system, then each of the four points is the orthocenter of the other three. These four possible triangles will all have the same nine point circle. Can you provide a simple way to prove this? — Preceding unsigned comment added by 81.152.49.127 (talk) 11:46, 5 March 2004 (UTC)
- sure. Fix 3 points and draw the triangle. The nine point circle will pass through the height feet (they're three out of the 9 points). Now, choose any other three, the lines are the same, so the height feet for the new triangle will be the same, thus the new ninepoint will pass throught the same 3 points (the height feet) and will be therefore the same. -- ( drini's page ☎ ) 22:34, 15 March 2006 (UTC)