Question: To find the diameter of any circle, construct the ________ to any chord on the circle. Congruent chord Perpendicular Parallel Perpendicular bisector Find the value of x. If necessary, round your answer to the nearest tenth. 23 7 x The graph shape is a circle with a horizontal chord near the top labeled 23, a radius drawn from the center perpendicular to the chord labeled 7, and another radius drawn from the center to the lower-right edge labeled x; position_hint ∈ bottom-right.

1. **State the problem:** We need to find the value of $x$ in a circle where a radius is drawn perpendicular to a chord of length $23$, and the perpendicular segment from the center to the chord is $7$. 2. **Recall the property:** The perpendicular from the center of a circle to a chord bisects the chord. This means the chord is divided into two equal segments of length $\frac{23}{2} = 11.5$. 3. **Set up the right triangle:** The radius $x$ is the hypotenuse of a right triangle formed by the perpendicular segment $7$ and half the chord $11.5$. 4. **Use the Pythagorean theorem:** $$ x^2 = 7^2 + 11.5^2 $$ 5. **Calculate:** $$ x^2 = 49 + 132.25 = 181.25 $$ 6. **Find $x$:** $$ x = \sqrt{181.25} \approx 13.5 $$ **Final answer:** $x \approx 13.5$ (rounded to the nearest tenth).