Question

1. find the value of x.

a. 10.0
b. 14.8
c. 11.3
d. 17.1

Explanation:

Step1: Analyze the circle properties

In a circle, if a radius (or a line from the center) is perpendicular to a chord, it bisects the chord. So the length of the half - chord is $\frac{16}{2}=8$.

Step2: Apply the Pythagorean theorem

We have a right triangle where one leg is 6 (the distance from the center to the chord), another leg is 8 (half of the chord length), and the hypotenuse is $x$ (the radius of the circle). By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 6$, $b = 8$, and $c=x$. So $x=\sqrt{6^{2}+8^{2}}$.

Step3: Calculate the value of $x$

First, calculate $6^{2}=36$ and $8^{2}=64$. Then $6^{2}+8^{2}=36 + 64=100$. So $x=\sqrt{100}=10.0$.

Answer:

A. 10.0