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Triangulation of an n-gon

Source: Swiss Math Olympiad 2010 - final round, problem 10

March 16, 2010
geometrycircumcircleinductioncombinatorics proposedcombinatorics

Problem Statement

Let n⩾3 n\geqslant 3 and P P a convex n n-gon. Show that P P can be, by n \minus{} 3 non-intersecting diagonals, partitioned in triangles such that the circumcircle of each triangle contains the whole area of P P. Under which conditions is there exactly one such triangulation?
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