Swing between Geometry and Algebra
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