# The nine-point-circle (Part I)

Geometry Level 5

For a triangle with sides 13, 15 and altitude 12, find the radius of the circle that pass through the following points:

• The midpoint of each side.

• The foot of each altitude.

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

If the radius can be written as $$a + \dfrac{m}{n}$$, where $$a,m$$ and $$n$$ are positive integers, $$m<n$$ and $$m$$ and $$n$$ are coprime. Find $$a+m+n$$.

Note: Assume the given altitude to be through the vertex common to both the given sides

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