In the given figure, ACDB is the diameter of the circle such that AC = CD = DB.Three semi-circles are drawn by taking AC, CD, and DB as diameters. What is the ratio of the area of shaded portion to the area of the non-shaded portion?

Let AC = CD = DB = 2r

Then, radius of each semi-circle = r

⇒ Radius of bigger circle = 2r + r = 3r

∴Area of bigger circle = π (3r)² = 9πr²

Area of each small semi-circle = $\frac{1}{2}{\mathrm{\pi r}}^2$

Area of the shaded region can be obtained by subtracting the areas of semi-circles with diameter AC and CD from the area of the bigger semi-circle and then adding the area of the semi-circle with diameter DB.

∴Area of shaded region = $\frac{1}{2}\times 9{\mathrm{\pi r}}^2-\left(\frac{1}{2}{\mathrm{\pi r}}^2+\frac{1}{2}{\mathrm{\pi r}}^2\right)+\frac{1}{2}{\mathrm{\pi r}}^2=4{\mathrm{\pi r}}^2$

⇒ Area of non-shaded region = 9πr² – 4πr² = 5πr²

∴ Required ratio = 4πr²:5πr² = 4: 5

Thus, the ratio of the area of the shaded region to the area of the non-shaded region is 4:5.