What type of triangle does Euler's nine point circle work with?

  • Thread starter Thread starter geometry
  • Start date Start date
  • Tags Tags
    Circle Point
AI Thread Summary
Euler's nine-point circle is applicable to all types of triangles, including acute, obtuse, and isosceles triangles. The discussion highlights a project on the nine-point circle, where the user faced issues constructing it with specific triangle types. A referenced resource suggests that the nine-point circle can indeed be constructed with various triangles. The confusion may stem from incorrect drawing techniques. Overall, the nine-point circle is versatile and works with any triangle configuration.
geometry
I'm doing a project on the nine point circle and i need to know what type of triangle it works with. I tried constructing it but it didn't work with an isoscoles or a obtuse triangle, but a website said it works with all triangles, can anyone help?
 
Mathematics news on Phys.org
Last edited:
The nine point circle works with general triangles. Maybe you're drawing something wrong.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

Similar threads

Replies
59
Views
2K
Replies
3
Views
3K
Replies
2
Views
2K
Replies
7
Views
2K
Replies
3
Views
1K
Replies
5
Views
2K
Back
Top