If the lines form a square, there is exactly one circle that fits, for each circle can be inscribed into a square; use a circle of the diameter that matches the square's height/width.
If the lines don't form a square, one can solve the algebraic equations or construct it "manually". Draw two lines that bi-sect the angle between two pairs of lines. Where these intersect is the centre of your circle. The radius of the circle is obtained by dropping a perpendicular line from the bisector intersection point as shown.
Greetings from the Easter bunny!
