Here are the steps for creating Orchtocenters for given triangles:
1) Constructing the ABC triangle:
2) Constructing the Orchtocenter of ABC triangle:
To find the Orchtocenter of ABC triangle, we must draw perpendicular lines from A, B, and C vertices to the three sides of ABC triangle. Our triangles' Orchtocenter will be the intersection point of these three perpendicular lines. As you can see below graph we draw perpendicular lines and H is the Orchtocenter of ABC triangle.
3) Constructing the Orcthocenter of HBC triangle:
As you see below graph vertices A is the Orcthocenter of HBC triangle.
4) Constructing the Orcthocenter of HAB triangle:
Vertices C is the Orcthocenter of HAB triangle.
5) Constructing the Orcthocenter of HAC triangle:
Vertices B is the Orcthocenter of HAC triangle.
6) Constructing circumcircles of ABC, HAB, HBC, and HAC triangles:
After we find Orcthocenters of given triangles, now we can find circumcircles of these triangles. Below you can see all circumcircles. When we connect all circumcircles then we get this graph.
