Question 59
The point $K$ lies in the interior of the unit circle. Four lines are drawn through $K$ such that each two adjacent lines form an angle of $45^{\circ}$, as shown in the picture. In such a way the circle is divided into 8 regions. Four of these regions are colored such that no two colored regions share more than one point. Find the maximal and minimal possible value for the total area of colored regions.
