MathDB
Putnam 2003 B5

Source:

June 23, 2011
Putnamgeometryanalytic geometrygeometric transformationrotationinequalitiescircumcircle

Problem Statement

Let AA, BB and CC be equidistant points on the circumference of a circle of unit radius centered at OO, and let PP be any point in the circle's interior. Let aa, bb, cc be the distances from PP to AA, BB, CC respectively. Show that there is a triangle with side lengths aa, bb, cc, and that the area of this triangle depends only on the distance from PP to OO.
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