Obtuse triangle

An obtuse triangle

An obtuse triangle is a triangle with an obtuse angle , that is, with an angle between 90 ° and 180 °. The longest side is opposite the obtuse angle.

Excellent points

As can be seen from the picture, in the case of the obtuse triangle of the four "classic" marked points, the intersection point (light brown) is so outside the triangle that it is closest to the corner point with the obtuse angle. The center of the circle (light green) is also outside the triangle, but on the other side, i.e. closest to the longest side. The center of gravity (dark blue) and the inscribed center point (red) lie within the triangle. ${\displaystyle H}$ ${\displaystyle U}$ ${\displaystyle S}$ ${\displaystyle I}$

The center of the Feuerbach circle (both light blue) is in the middle of the line and, depending on the shape of the triangle, inside or outside the triangle. There are nine excellent points on the Feuerbach district . These are the side center points and the center points of the so-called upper height sections and as well as the height base points and ${\displaystyle F}$ ${\displaystyle {\overline {HU}}}$ ${\displaystyle J,M}$ ${\displaystyle O,}$ ${\displaystyle E,K}$ ${\displaystyle N}$ ${\displaystyle D,G}$ ${\displaystyle L.}$

The designations of the marked points and their positions are comparable to those of the acute-angled triangle .

The points , , and are, as with all triangles on the Euler straight (red). ${\displaystyle U}$ ${\displaystyle S}$ ${\displaystyle F}$ ${\displaystyle H}$ ${\displaystyle e}$

Obtuse triangle with the four "classic" excellent points , , and , moreover, the center of the Feuerbach circle with its nine excellent points and the Euler line ${\displaystyle U}$ ${\displaystyle S}$ ${\displaystyle I}$ ${\displaystyle H,}$ ${\displaystyle F}$ ${\displaystyle e.}$

See also

• triangle
• Equilateral triangle
• Isosceles triangle
• Right triangle
• Acute triangle
• Excellent points in the triangle

Web links

• Eric W. Weisstein : Obtuse Triangle . In: MathWorld (English).

Individual evidence

1. ↑ Arne Madincea: The Feuerbach Circle… The sentence about the 9-point circle: Exercise 1, p. 2 ff. (PDF) In: Materials for mathematics lessons. Herder-Gymnasium Berlin, p. 7 , accessed on November 25, 2018 .