Question

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Explanation:

Step1: Apply the perpendicular - chord bisector theorem

If a diameter is perpendicular to a chord, then it bisects the chord. Let the radius of the circle be \(r = 20\). Let the length of the half - chord be \(l=16.2\), and the distance from the center of the circle to the chord be \(d = x\).

Step2: Use the Pythagorean theorem in the right - triangle formed

In a circle, if a radius \(r\), half - chord length \(l\), and the distance from the center of the circle to the chord \(d\) form a right - triangle, then \(r^{2}=l^{2}+d^{2}\). Substitute \(r = 20\) and \(l = 16.2\) into the formula: \(d=\sqrt{r^{2}-l^{2}}\).

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Answer:

\(x = 11.73\)