Challenge 43: The Euler Segment of a Triangle
The relationships presented in this challenge seem quite surprising. However, they are results of the dependencies imposed in the triangle by the constructions of the different centers.
Sometimes combinations of complex dependencies have surprising results.
A Swiss mathematician named Euler (his last name is pronounced “oiler”) discovered a relationship among three of the centers that you created in the previous activities.
Can you discover what he did?
He did this in the 1700s—without dynamic-geometry tools.
Euler’s work renewed interest in geometry and led to many discoveries beyond Euclid’s.