Problems

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Found: 7

On the planet Tau Ceti, the landmass takes up more than half the surface area. Prove that the Tau Cetians can drill a hole through the centre of their planet that connects land to land.

The opposite sides of a convex hexagon are pairwise equal and parallel. Prove that it has a centre of symmetry.

A parallelogram \(ABCD\) and a point \(E\) are given. Through the points \(A, B, C, D\), lines parallel to the straight lines \(EC, ED, EA,EB\), respectively, are drawn. Prove that they intersect at one point.

A quadrilateral has an axis of symmetry. Prove that this quadrilateral is either an isosceles trapezoid or is symmetric with respect to its diagonal.