Geometry Problems, Online Education

Geometry Problem 159: The Fascinating Relationship between Circumradius and Distances from Circumcenter and Excenters of a Triangle. Level: High School, College, Mathematics Education

Prove that the sum of the squares of the distances from the circumcenter to the incenter and the three excenters of a triangle is equal to 12 times the square of the circumradius.

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Triangle distance centers

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