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Problem #PRU-116573

Problems Geometry Plane geometry Circles Diameter, chords, and secants Chords and secants (other) Polygons Regular polygons

What is the maximum number of pairwise non-parallel segments with endpoints at the vertices of a regular \(n\)-gon?

Problem #PRU-98408

Problems Geometry Plane geometry Circles Central angle. Arc length and circumference Diameter, chords, and secants Chords and secants (other) Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Polygons Regular polygons

In a regular shape with 25 vertices, all the diagonals are drawn.

Prove that there are no nine diagonals passing through one interior point of the shape.