1) switch to the Select-on-contour-tool (press CTRL+2)

2) pick-move point Y

3) p' changes but not his area (displayed in the number-object)

4) switch to selection-tool (press CTRL+1)

5) pick X and drag to enlarge the inner circle. Repeat the experiments

6) Notice the existence of a critical radius OZ, so that p' is convex only if OX is less than OZ

7) Calculate OZ

8) Make c' greater than c and the polygon p' non-convex

9) Repeat the experiments for such a configuration

10) What is the area of a non-convex polygon with self-intersections?

11) Prove the proposition

For the proof of a generalization look at the file PedalPolygons.html .

PedalPolygons.html

SquaresCombination.html

Stewart.html

WeightedSumsOfDistances.html

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