Question

9 multiple choice 1 point in circle d, which of the following is an example of a chord? 10 multiple choice 1 point find the shortest distance from the center of the circle, c, to the line rs. the length of segment rs is 8 in. the diameter of the circle is 20 in.

Explanation:

Step1: Recall the definition of a chord

A chord is a line segment with both endpoints on the circle.

Step2: Analyze each option

• \(DE\): \(D\) is the center, \(E\) is on the circle. So \(DE\) is a radius (not a chord).
• \(DG\): \(D\) is the center, \(G\) is on the circle. So \(DG\) is a radius (not a chord).
• \(FG\): \(F\) and \(G\) are both on the circle. So \(FG\) is a chord.
• \(DF\): \(D\) is the center, \(F\) is on the circle. So \(DF\) is a radius (not a chord).

for problem 10:

Step1: Find the radius of the circle

The diameter \(d = 20\) in, so the radius \(r=\frac{d}{2}=10\) in.

Step2: Use the perpendicular - distance formula from the center to a chord

Let the distance from the center \(C\) to the chord \(RS\) be \(d\). If the length of the chord \(RS = l=8\) in, and the radius \(r = 10\) in. We know that the perpendicular from the center to a chord bisects the chord. So the half - length of the chord \(x=\frac{l}{2}=\frac{8}{2} = 4\) in.
By the Pythagorean theorem \(d=\sqrt{r^{2}-x^{2}}\) (where \(r\) is the radius of the circle and \(x\) is the half - length of the chord).
Substitute \(r = 10\) and \(x = 4\) into the formula: \(d=\sqrt{10^{2}-4^{2}}=\sqrt{100 - 16}=\sqrt{84}=2\sqrt{21}\) in.

Answer:

C. \(FG\)