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Found: 4

Problems Discrete Mathematics Set theory and logic Mathematical logic Paradoxes Geometry Plane geometry Quadrilateral Parallelogram Special cases Rectangles and squares. Criteria and properties

The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?

Problem #PRU-64622

Problems Algebra Polynomials Algebraic identities for polynomials Identical transformations Geometry Plane geometry Quadrilateral Inscribed quadrilaterals

13–15 3.0

The number \(x\) is such a number that exactly one of the four numbers \(a = x - \sqrt{2}\), \(b = x-1/x\), \(c = x + 1/x\), \(d = x^2 + 2\sqrt{2}\) is not an integer. Find all such \(x\).

Problem #PRU-86112

Problems Geometry Plane geometry Quadrilateral Arbitrary quadrilaterals Algebra Trigonometry Trigonometry (other)

14–15 2.0

Does there exist a flat quadrilateral in which the tangents of all interior angles are equal?

Problem #PRU-57006

Problems Geometry Plane geometry Quadrilateral Circumscribed quadrilaterals

13–16 4.0

Prove that a convex quadrilateral \(ICEF\) can have a circle inscribed into it if and only if \(IC+EH = CE+IF\).