Will you please share the previous year Questions with answers of RMO - Regional Mathematical Olympiads????

Here I am sharing the previous year Questions with answers of RMO - Regional Mathematical Olympiads

Let ABCD be a unit square. Draw a quadrant of a circle with A as centre and B;D

as end points of the arc. Similarly, draw a quadrant of a circle with B as centre and

A;C as end points of the arc. Inscribe a circle

Let X = f1; 2; 3; : : : ; 12g. Find the the number of pairs fA;Bg such that A X,

B X, A 6= B and A \ B = f2; 3; 5; 7; 8g.

Let a and b be positive real numbers such that a + b = 1. Prove that

aabb + abba lessert then equal to 1: