The circle x² + y² - 2x = 0 is partitioned by line y = x in two segments. Let A₁, A₂ be the areas of major and minor segments respectively. What is the value of 2(A₁ + A₂)/(A₁ - 3A₂)?

From the previous problem, A₁ + A₂ = total area of circle = π(1)² = π. With A₁ = (3π+2)/4 and A₂ = (π-2)/4, we have A₁ - 3A₂ = (3π+2)/4 - 3(π-2)/4 = (3π+2 - 3π+6)/4 = 8/4 = 2. Therefore 2(A₁+A₂)/(A₁-3A₂) = 2π/2 = π.