The figure below shows a circle drawn inside a square. A shaded square is then drawn inside the circle. What fraction of the figure is shaded? Ans : ___

1. Express the area of the outer square in terms of the circle's radius

Let the radius of the circle be $r$.
The circle is inscribed in the outer square, so the side length of the outer square is equal to the diameter of the circle, which is $2r$.
Area of outer square = $(2r)^2 = 4r^2$.

2. Express the area of the inner shaded square in terms of the circle's radius

The inner shaded square is inscribed in the circle, so its diagonal is equal to the diameter of the circle, which is $2r$.
Area of inner square = $\frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 = \frac{1}{2} \times (2r) \times (2r) = 2r^2$.

3. Calculate the fraction of the figure that is shaded

Fraction shaded = $\frac{\text{Area of inner square}}{\text{Area of outer square}} = \frac{2r^2}{4r^2} = \frac{1}{2}$.