1. **State the problem:** We need to find the value of $x$ in a circle where a chord segment $x$ is related to two other segments: one radius segment of length 4.9 and a chord segment of length 5.3. 2. **Identify the relevant formula:** In circle geometry, if a radius is perpendicular to a chord, it bisects the chord. This means the chord is divided into two equal parts. 3. **Apply the rule:** Since the radius of length 4.9 is drawn to the chord, it bisects the chord into two equal segments. The total chord length is 5.3, so each half is $\frac{5.3}{2}$. 4. **Calculate each half:** $$ \frac{5.3}{2} = 2.65 $$ 5. **Relate to $x$:** The segment $x$ is one half of the chord, so $$ x = 2.65 $$ 6. **Final answer:** $$ x = 2.65 $$