1. **Stating the problem:** We have a circle with several line segments from points on the circle to a central point, forming right angles. The segments are labeled 18.2, 19.4, 6.6, and $x$. We need to find the value of $x$. 2. **Understanding the problem:** The right-angle marker near the center suggests the segments form right triangles or are related by the Pythagorean theorem. 3. **Using the Pythagorean theorem:** For right triangles, the sum of the squares of the legs equals the square of the hypotenuse. 4. **Setting up the equation:** Given the segments 18.2, 19.4, 6.6, and $x$, and the right angle at the center, we can write: $$18.2^2 + x^2 = 19.4^2$$ assuming $x$ and 18.2 are legs and 19.4 is the hypotenuse. 5. **Calculating squares:** $$18.2^2 = 331.24$$ $$19.4^2 = 376.36$$ 6. **Substitute values:** $$331.24 + x^2 = 376.36$$ 7. **Isolate $x^2$:** $$x^2 = 376.36 - 331.24$$ $$x^2 = 45.12$$ 8. **Find $x$ by taking the square root:** $$x = \sqrt{45.12}$$ 9. **Calculate the square root:** $$x \approx 6.71$$ 10. **Final answer:** $$\boxed{6.71}$$ This means the length of segment $x$ is approximately 6.71 units.