Swing between Geometry and Algebra

Geometry Level 4

Geometric median of three points in Euclidean plane is also known as Fermat point. One such problem was given by Pierre de Fermat to Evangelista Torricelli in c.1644.

In a triangle ∆ABC with side lengths 5, 12 and 13, there is a point O such that the total distance from the three vertices of the triangle to the point is the minimum possible i.e. p = OA + OB + OC. If p^2 = m + n√3 , then m + n is equal to

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