Showing posts with label nine point circle. Show all posts
Showing posts with label nine point circle. Show all posts

Saturday, September 1, 2012

The Euler Line

In the figure below, the green, red, and violet 'points' are the orthocenter, centroid, and circumcenter of triangle ABC respectively. Move the points A, B, and C and notice what happens. Use these points to create different types of triangles. What do you observe? This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
The blue line above is called the Euler line. The Euler line passes through the three important points determine by a non-equilateral triangle. It also passes through the center of the nine point circle.

Monday, April 11, 2011

The Nine-Point Circle

Move the vertices of the triangle and observe what happens.


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

The nine-point circle is the circle passing through the nine significant points defined from a triangle. It includes the midpoint of each side, the foot of each altitude, and the midpoints of the orthocenter and the three vertices.