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 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...

Try this beautiful problem from the Pre-RMO, 2017 based on Ordered triples. Ordered Triples – PRMO 2017 What is the number of triples (a,b,c) of positive integers such that abc=108? is 107is 60is 840cannot be determined from the given information Key Concepts...

Try this beautiful problem from PRMO, 2019 based on Ratio of the areas. Ratio of the areas | PRMO | Problem-19 Let $\mathrm{AB}$ be a diameter of a circle and let $\mathrm{C}$ be a point on the segment $\mathrm{AB}$ such that $\mathrm{AC}: \mathrm{CB}=6: 7 .$ Let...

Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral. Sides of Quadrilateral – PRMO 2017 What is the number of triples (a,b,c) of positive integers such that (i) a<b<c<10 and (ii) a,b,c,10 form the sides of a quadrilateral?...

Try this beautiful problem from the Pre-RMO, 2019 based on rearrangement. Rearrangement Problem – PRMO 2019 We will say that the rearrangement of the letters of a word has no fixed letters if. When the rearrangement is placed directly below the word, no column...