1. **State the problem:** We have a circle with radius $r$ and points $A$, $F$, $O$, $B$, and $G$ arranged such that $\triangle ABO$ and $\triangle GOF$ are right triangles inside the circle. We want to find the area of the shaded region formed by parts of these triangles and the circle. 2. **Identify the shapes and areas involved:** The circle has area $$\pi r^2$$. 3. **Analyze the right triangles:** Each right triangle inside the circle has legs of length $r$ (since points lie on the circle and center $O$ is at the origin). The area of each right triangle is $$\frac{1}{2} r^2$$. 4. **Determine the shaded region:** The shaded region is the part of the circle excluding the two right triangles. Since the two right triangles are inside the circle and do not overlap, their combined area is $$2 \times \frac{1}{2} r^2 = r^2$$. 5. **Calculate the shaded area:** $$\text{Shaded area} = \text{Area of circle} - \text{Area of two triangles} = \pi r^2 - r^2 = r^2 (\pi - 1)$$ 6. **Conclusion:** The area of the shaded region is $$r^2 (\pi - 1)$$. This matches the option $r^2(\pi - 1)$.