We would like to start our expolaration with following constructions:

1) Construct any triangle ABC and construct the orthocenter of ABC

__We observed that the orthecenters of
triangles HAC, HAB and HBC are B,C and A (one of the vertexesof
the original triangle ABC)__

__Click here to see animation
........................Click here to see animation__

__the length
of four circles are the same anyhow we move original ABC triangle.__

It was named by French Mathematician Jean-Victor Poncelet. Karl Feuerbach made many expolaration with nine-point circle.

** ma,mb and mc**, and

point( center of nine-point triangle)
lies on the same line which passes through

** ABC **triangle.
They are also tangent to the nine-point circle.

We found that the nine-point circles of the triangles,ABC,HAC,HAB and HBC are the same.

The interesting observation is : .That is true all different possible triangles.