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Found: 3

Problem #PRU-32032

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Linear inequalites and systems of inequalities Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Geometry Plane geometry Geometrical inequalities Triangle inequality Triangle inequality (other)

13–14 3.0

On a plane, there are 1983 points and a circle of unit radius. Prove that there is a point on the circle, from which the sum of the distances to these points is no less than 1983.

Problem #PRU-55146

Problems Geometry Plane geometry Geometrical inequalities Triangle inequality Triangle inequality (other)

13–14 2.0

In an isosceles triangle, the sides are equal to either 3 or 7. Which side length is the base?

Problem #PRU-79403

Problems Geometry Plane geometry Geometrical inequalities Triangle inequality Triangle inequality (other) Visual geometry

13–15 4.0

In a square with side length 1 there is a broken line, which does not self-intersect, whose length is no less than 200. Prove that there is a straight line parallel to one of the sides of the square that intersects the broken line at a point no less than 101 units along the line.