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When two triangles have the same orthocenter and circumscribing circle, are the nine points are the same too? If two triangles have the same circumscribing circle, at least the sides have the same length?

Could you please give me some explanation for this? Thanks!

Student
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  • are the nine points are the same too...could you elaborate? What 9 points? – Guy Mar 25 '14 at 15:52
  • Oh, I meant nine points from the nine point circle. – Student Mar 25 '14 at 15:54
  • This kind of question is very interesting ! See: http://math.fau.edu/yiu/YiuConicSolutionEuler.pdf and http://forumgeom.fau.edu/FG2011volume11/FG201112.pdf – Alan Mar 25 '14 at 20:03

1 Answers1

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Trick Question:

If the orthocenter is the same point as the centre of the circumscribing circle, then the triangle is equilateral , and all equilateral triangles are similar to eachother.

Willemien
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