Question

1. a chord 24 inches long is 5 inches from the center of a circle, as shown below. what is the radius of the circle, to the nearest tenth of an inch? a. 29.0 b. 24.5 c. 16.9 d. 13.0 e. 10.9

Explanation:

Step1: Divide the chord in half

The perpendicular from the center of a circle to a chord bisects the chord. So half - length of the chord $a=\frac{24}{2}=12$ inches. The distance from the center of the circle to the chord $b = 5$ inches.

Step2: Apply the Pythagorean theorem

In the right - triangle formed by the radius $r$, half of the chord, and the line from the center to the chord, we have $r^{2}=a^{2}+b^{2}$ according to the Pythagorean theorem. Substitute $a = 12$ and $b = 5$ into the formula: $r^{2}=12^{2}+5^{2}=144 + 25=169$.

Step3: Solve for the radius

Take the square root of both sides of the equation $r^{2}=169$. So $r=\sqrt{169}=13.0$ inches.

Answer:

D. 13.0