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An alluring 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...

I.S.I Entrance-2013 problem 2

Understand the problem For x ≥ 0 definef(x) =.Determine the set {y ∈ R : y = f(x), x ≥ 0}. Source of the problem I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2013. Subjective Problem no. 2. Topic Calculus , Function  Difficulty Level...

A function on squares

Understand the problem Let  be a real-valued function on the plane such that for every square  in the plane,  Does it follow that  for all points  in the plane? Source of the problem Putnam 2009 A1 Topic Geometry Difficulty Level Easy Suggested Book Mathematical...

Extremal Principle : I.S.I Entrance 2013 problem 4

Understand the problem In a badminton singles tournament, each player played against all the othersexactly once and each game had a winner. After all the games, each playerlisted the names of all the players she defeated as well as the names of all theplayers defeated...

Lattice point inside a triangle

Understand the problem Given a triangle ABC with three lattice vertices . it is known that no more lattice point lies on the edges . only one lattice point D is inside the triangle . prove that D is centroid of that triangle .     Source of the problem Iran Maths...

An isosceles triangle,on Trigonometry, I.S.I Entrance 2016, Solution to Subjective problem no. 6

Understand the problem Let (a,b,c) be the sides of a triangle and (A,B,C) be the angles opposite to those sides respectively. If ( sin (A-B)=frac{a}{a+b}sin Acos B-frac{b}{a+b} cos A sin B), then prove that the triangle is isosceles. Source of the problem I.S.I....