Try this beautiful problem from PRMO, 2019, Problem 18 based on Ordered Pairs. Orderd Pairs | PRMO | Problem-18 How many ordered pairs \((a, b)\) of positive integers with \(a < b\) and \(100 \leq a\), \(b \leq 1000\) satisfy \(gcd (a, b) : lcm (a, b) = 1 : 495\) ?...

Try this beautiful problem from PRMO, 2019 based on Maximum area Maximum area | PRMO-2019 | Problem-23 Let $\mathrm{ABCD}$ be a convex cyclic quadrilateral. Suppose $\mathrm{P}$ is a point in the plane of the quadrilateral such that the sum of its distances from the...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on Complex Plane. Problem on Complex Plane – AIME I, 1988 Let w_1,w_2,….,w_n be complex numbers. A line L in the complex plane is called a mean line for...

Try this beautiful problem from Geometry based on Rectangle Pattern from AMC 10A, 2016, Problem 10. Rectangle Pattern- AMC-10A, 2016- Problem 10 A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic...

Try this beautiful problem from Geometry based on ratio of Circles from AMC 10A, 2009, Problem 21. Ratio of Circles – AMC-10A, 2009- Problem 21 Many Gothic cathedrals have windows with portions containing a ring of congruent circles that are circumscribed by a...

Try this beautiful problem from the Pre-RMO, 2019 based on Covex Cyclic Quadrilateral. Covex Cyclic Quadrilateral – PRMO 2019 Let ABCD be a convex cyclic quadrilateral. Suppose P is a point in the plane of the quadrilateral such that the sum of its distance from...