For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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8
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1answer
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can a convex polygon have only one boundary point at locally maximum distance from its centroid?

It's easy to see that given any convex polygon P and any point c in its interior, there is at least one point m on the boundary of P at locally maximum distance from c: simply choose m to be a vertex ...
6
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1answer
80 views
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How to prove this geometry inequality (1) with $2(DF+EF)\ge BC$

There is a picture which hope to illustrate the configuration $\Delta ABC$,such $\angle A=\dfrac{2\pi}{3}$ ,and $F$ is middpoint on $BC$,and $D,E$ on the $AB,AC$ respectily,such $DE//BC$ show that ...