1. Let x and y be real numbers such that x^2 + y^2 = 4(x + y). Find the largest possible value of x.
2. The lines y = x/3 and y = 13x/9 are drawn in the coordinate plane. Find the slope of the line that bisects the angle between these lines.
1. The maximum value of x is 5 + sqrt(3).
2. Using the angle bisector theorem, I found that the slope of the line in the middle is 7/5.
