Problem 2

Part of 2008 SEEMOUS

Problems(1)

sequences of polygons, vertices are midpoints of sides, convergence

Source: SEEMOUS 2008 P2

P_0,P_1,P_2,\ldots

be a sequence of convex polygons such that, for each

k\ge0

, the vertices of

P_{k+1}

are the midpoints of all sides of

P_k

. Prove that there exists a unique point lying inside all these polygons.

Sequencesgeometryconvex polygon