The nine-point-circle (Part II)

Geometry Level 5

A circle pass through the following points in a triangle

  • The midpoint of each side.

  • The foot of each altitude.

  • The midpoint of the line segment from each vertex of the triangle to the orthocenter.

Find the perimeter of the triangle for which the radius of such circle is 10. Assume the triangle to have integer sides and area.


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