Hidden triangular inequality (PRMO Problem 23, 2019)

Problem Let ABCD be a convex cyclic quadrilateral . Suppose P is a point in the plane of the quadrilateral such that the sum of its distances from the vertices of ABCD is the least .If {PA,PB,PC,PD} = {3,4,6,8}.What is the maximum possible area of ABCD? TopicGeometry...

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

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

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...

I.S.I 2016 SUBJECTIVE PROBLEM – 1

Understand the problem Suppose that in a sports tournament featuring n players, each pairplays one game and there is always a winner and a loser (no draws).Show that the players can be arranged in an order P1, P2, . . . , Pn suchthat player Pi has beaten Pi+1 for all...