The nine-point-circle
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
by
Digvijay Singh