**Assignment #8**

**Altitudes and Orthocenters**

By

**Michelle
Nichols**

Construct any triangle ABC.

Construct the Orthocenter H of triangle ABC.

Construct segments between H and all vertices of triangle
ABC, to get Triangle **HBC**, **HAB**, and **HAC**.

If we construct the orthocenters of each of these
triangles, each will have an orthocenter the same as a vertice of Triangle
ABC.

**For Triangle HBC, the Orthocenter is Point A**

**For Triangle HAB, the Orthocenter is Point C**

**For Triangle HAC, the Orthocenter is Point B**

Now, construct the circumcircles for all triangles: ABC,
HBC, HAB, and HAC.

What if we look at the nine-point circle?

Triangles ABC, HBC, HAB, and HAC all share the same