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Sum of Radii (Posted on 2008-03-12) Difficulty: 4 of 5
Let ABC be an arbitrary triangle and O, r, and R its circumcenter, inradius, and circumradius respectively.
Let OA, OB, and OC be the midpoints of sides BC, CA, and AB respectively.

For X = A, B, and C let

     SX = |OOX|  if the line segment OOX intersects
                 the interior of triangle ABC,

        = -|OOX| otherwise.
Prove that r + R = SA + SB + SC.

See The Solution Submitted by Bractals    
Rating: 3.6667 (3 votes)

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  Subject Author Date
SolutionTriangle trigonometryChesca Ciprian2008-03-13 16:11:17
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