This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 28

1969 Polish MO Finals, 3
Tags: geometry , octagon , rational , symmetry
Prove that an octagon, whose all angles are equal and all sides have rational length, has a center of symmetry.

1975 Chisinau City MO, 110
Tags: octagon , symmetry , geometry
Prove that any centrally symmetric convex octagon has a diagonal passing through the center of symmetry that is not parallel to any of its sides.

1967 Vietnam National Olympiad, 3
Tags: geometry , rhombus , octagon , incircle , construction
i) $ABCD$ is a rhombus. A tangent to the inscribed circle meets $AB, DA, BC, CD$ at $M, N, P, Q$ respectively. Find a relationship between $BM$ and $DN$. ii) $ABCD$ is a rhombus and $P$ a point inside. The circles through $P$ with centers $A, B, C, D$ meet the four sides $AB, BC, CD, DA$ in eight points. Find a property of the resulting octagon. Use it to construct a regular octagon. iii) Rotate the figure about the line $AC$ to form a solid. State a similar result.