Bangladesh Mathematical Olympiad 2024 Solution  #2

Question:

The perimeter of a triangle with side lengths of ( 1.5π,  2.5π, and  2π is equal to the circumference of the circle with center  O . In the figure,  AB = BC = 2√2. If the area of  OABC  can be written as ( a√b), then find the value of  a + b .