More on the Euler Line

Geometry Level 4

A triangle with circumradius R = 8 10 R = 8\sqrt{10} has its orthocenter O O at ( 3 , 4 ) \left( 3,4 \right) and a vertex at ( 5 , 10 ) \left( 5,10 \right) that lies on its Euler line. If the triangle's circumcenter is closer to the orthocenter than it is to the known vertex, and the area of this triangle is given by A B A\sqrt{B} where B B is a prime number, what is A + B A+B ?


The answer is 277.

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