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

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Does there exist regular planar pentagon?

How to prove or disprove that the boundary of any convex body in $\mathbb{R}^3$ (treated as a surface) includes 5 points which form a regular planar pentagon?
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Viviani's theorem using Pythagoras

Did anyone find the proof of Viviani's Theorem just by using Pythagoras' relations in the triangles? Thanks.