Question

x 37.4 17.1

Explanation:

Step1: Apply the perpendicular - bisector theorem

The perpendicular from the center of a circle to a chord bisects the chord. Let the radius of the circle be \(r = 37.4\), half - chord length \(l=17.1\), and the distance from the center to the chord be \(x\).

Step2: Use the Pythagorean theorem

In the right - triangle formed by the radius (hypotenuse), half - chord, and the line from the center to the chord (one of the legs), we have \(r^{2}=x^{2}+l^{2}\). Substitute \(r = 37.4\) and \(l = 17.1\) into the formula: \(x=\sqrt{r^{2}-l^{2}}\).

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Answer:

\(x\approx33.3\)