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Found: 34

Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle A perpendicular distance is the shortest. Inequalities for right triangles

13–13 2.0

\(ABC\) is a right angled triangle with a right angle at \(C\). Prove that \(c^n > a^n + b^n\) for \(n > 2\).

Problem #PRU-58082

Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle A segment inside the triangle is smaller than the largest side ,Problems Geometry Plane geometry Triangles Types of triangles Right-angled triangles Pythagorean theorem and its converse

12–14 4.0

A \(3\times 4\) rectangle contains 6 points. Prove that amongst them there will be two points, such that the distance between them is no greater than \(\sqrt5\).

Problem #PRU-65268

Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle A segment inside the triangle is smaller than the largest side ,Problems Probability and statistics Probability theory Discrete distribution

13–16 3.0

There are 25 children in a class. At random, two are chosen. The probability that both children will be boys is \(3/25\). How many girls are in the class?

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.