Question

find the length of the chord x, in centimeters, that is 6 centimeters from the center of a circle that has a radius of 10 centimeters.

Explanation:

Step1: Apply the Pythagorean theorem

In a right - triangle formed by the radius (hypotenuse \(r = 10\) cm), the distance from the center to the chord (\(d=6\) cm), and half of the chord (\(l\)). By the Pythagorean theorem \(l=\sqrt{r^{2}-d^{2}}\).
Substitute \(r = 10\) and \(d = 6\) into the formula: \(l=\sqrt{10^{2}-6^{2}}\).

Step2: Calculate the value of \(l\)

First, calculate \(10^{2}-6^{2}=100 - 36=64\). Then \(\sqrt{64}=8\).

Step3: Find the length of the chord \(x\)

Since \(x = 2l\) (the perpendicular from the center of a circle to a chord bisects the chord), and \(l = 8\), then \(x=2\times8 = 16\).

Answer:

16