Special points and lines in a triangle
Below you find a triangle with the option to visualise certain special points and lines in a triangle.
The triangle's vertices can be dragged to form different triangles.
Experiment with the different lines and their intersections.
The special circles for the triangle you can look at (incircle and circumcircle will be studied later in the lecture)
Some questions for exploration
Here are some questions that you can think about....
1. The orthocenter is the intersection of the altitudes.
How do triangles look like whose orthocenters lie outside of the triangle
2. The centroid (center of gravity) splits each median into a certain ratio. What is the ratio and why is it so?
3. Can the centroid lie outside of the triangle?
4. Are there three of the centers which are collinear for all triangles?