Acute triangle

An acute triangle

An acute triangle is a triangle in which all angles are less than 90 °. The three sides do not have to be of different lengths.

Excellent points

In the acute-angled triangle are the four "classic" points , the center of the circle (light green), the center of gravity (dark blue), the center of the inscribed circle (red) and the intersection point (light brown) as well as the center of the Feuerbach circle (both light blue), within the triangle. ${\displaystyle U}$ ${\displaystyle S}$ ${\displaystyle I}$ ${\displaystyle H}$ ${\displaystyle F}$

There are nine excellent points on the Feuerbach district . In the picture these are the side centers and the centers of the so-called upper height sections and as well as the height base points and ${\displaystyle J,M}$ ${\displaystyle O,}$ ${\displaystyle E,K}$ ${\displaystyle N}$ ${\displaystyle D,G}$ ${\displaystyle L.}$

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

Acute 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
• Obtuse triangle
• Excellent points in the triangle

Web links

• Eric W. Weisstein : Acute 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 .