Geometry · Circumcircle · Cyclic quadrilateral · Extremal problem · Triangle inequality
Find all points \(P\) on the circle circumscribed about a triangle \(ABC\) for which the sum
\[ PA + PB + PC \]
is as small as possible.
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Serbian Regional Competition 2005, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source