Classical Triangle Centres and Circles.
- Author:
- CharlyM
- Topic:
- Circle, Median Line
This shows the construction of a few of the classic triangle centres, and explains their properties.
It show's that the Orthocentre, the Centroid and the Circumcentre lie on the Euler line, and how they are positioned.
It show's how the ninepoint circle is constructed and explains its properties.
It shows the excircles, and demonstrates that the ninepoint circle is tangent to these and the incircles.
Checkboxes allow the user to show only the basic constructions required for each of the demonstrations, or to superimpose further detail as required.
P.S. I had quite a bit of fun reminding myself of all this stuff from schooldays, and playing around with Geogebra, which is soo much more fun than rules and compases! I also found an article in Wikepedia [url][/http://en.wikipedia.org/wiki/Isogonal_conjugate] which explained that the Orthocentre and the Circumcentre are Complements (Isogonal Conjugates). The concepts of Isogonal Conjugates looked simple, and thought at first it would have been easy to add this as well ... but when I tried the construction I found it didn't work ... have I gone wrong somewhere I wonder? Would be delighted if someone would take the next step.