Nine Point Circle Construction 

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First construct a triangle.
Then construct the midpoints of the sides of this triangle.
Now join these points
Now construct the circumcentre of this smaller triangle.
This is the ninepoint circle of the triangle ABC. To construct the other 6 points, you need to find the altitudes of ABC. The feet of these altitudes gives you the first 3 points.
The altitudes intersect in the orthocentre of ABC. Midpoints of the lines which connect orthocentre with the vertices A, B, and C, will give you further 3 points.
Click here to find more about the Nine Point Circle.

Learn more about Circle here or about various properties of triangles: Learn more about Euler or some other famous mathematicians. Some interesting mathematical artefacts can be found here! Mathematicians' delights and possessions... 

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