MathDB
polygon's area doesn't add much when combined with its centric symmetry

Source: 2021ChinaTST test4 day2 P2

April 14, 2021
geometrycombinatorial geometrycombinatoricsareaConvex hullconvex polygonsymmetry

Problem Statement

Find the smallest real α\alpha, such that for any convex polygon PP with area 11, there exist a point MM in the plane, such that the area of convex hull of P∪QP\cup Q is at most α\alpha, where QQ denotes the image of PP under central symmetry with respect to MM.
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