Question 21
A disk $K$ with radius $R$ is divided into three circular sectors so that the sum of the areas of the two smaller sectors equals the area of the largest sector, and the difference of the areas of the two smaller sectors equals one third of the area of the largest sector. In each of the sectors we inscribe the largest possible disk, and we denote these disks by $K_{1}, K_{2}$ and $K_{3}$. Express the area of the region $K \backslash\left(K_{1} \cup K_{2} \cup K_{3}\right)$ in terms of the parameter $R$.