A trigonometric relation and its implication

A trigonometric relation and its implication

Understand the problem Prove that a triangle is right-angled if and only if Source of the problem Vietnam National Mathematical Olympiad 1981 Topic Trigonometry Difficulty Level Medium Suggested Book Challenge and Thrill of Pre-college Mathematics Start with hints...
A polynomial equation and roots of unity

A polynomial equation and roots of unity

Understand the problem Find all polynomials with real coefficients such that divides . Source of the problem Indian National Mathematical Olympiad 2018 Topic Algebra Difficulty Level Easy Suggested Book Problem Solving Strategies by Arthur Engel Start with hints...
Bicentric quadrilaterals inside a triangle

Bicentric quadrilaterals inside a triangle

Understand the problem Let be a triangle and be cevians concurrent at a point . Suppose each of the quadrilaterals and has both circumcircle and incircle. Prove that is equilateral and coincides with the center of the triangle. Source of the problem Indian team...
Trilinear coordinates and locus

Trilinear coordinates and locus

Understand the problem Let be an equilateral triangle and in its interior. The distances from to the triangle’s sides are denoted by respectively, where . Find the locus of the points for which can be the sides of a non-degenerate triangle. Source of the...
A sequence of (mostly) prime numbers

A sequence of (mostly) prime numbers

Understand the problem Find all pairs of positive integers, such that the sequence defined by , and for has only finite number of composite terms. Source of the problem Bulgarian Mathematical Olympiad 2002 Topic Number theory Difficulty Level Medium Suggested Book...