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A stability theorem for the area sum of a convex polygon and its polar reciprocal. (English) Zbl 0913.52002
The author proves a stability theorem regarding the following result: for $$P$$ a planar, convex polygon inscribed in the unit circle $$K$$ and $$P^*$$ its polar reciprocal with respect to $$K$$, the area sum of both polygons is larger than or equal to $$G$$, with equality only if $$P$$ is a square.
##### MSC:
 52A40 Inequalities and extremum problems involving convexity in convex geometry 52A10 Convex sets in $$2$$ dimensions (including convex curves)
##### Keywords:
polar reciprocal; area sum; stability result; convex polygon
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