Question

find the length of the segment indicated. round to the nearest tenth if necessary. value: 10 = 8/8 < prev next >

Explanation:

1. First, identify the relevant geometric property:

• In a circle, if a radius is perpendicular to a chord, it bisects the chord. Let the radius of the circle be \(r = 5\), and the distance from the center of the circle to the chord be \(d = 3\).
• We can use the Pythagorean - theorem in the right - triangle formed by the radius, half of the chord, and the line from the center of the circle perpendicular to the chord.
• Let half of the chord length be \(l\). According to the Pythagorean theorem \(l=\sqrt{r^{2}-d^{2}}\).

1. Then, substitute the values of \(r\) and \(d\) into the formula:

• Given \(r = 5\) and \(d = 3\), we have \(l=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\).
• The length of the chord (the segment indicated) is \(x = 2l\).
• So \(x = 8\).

Answer:

8