Consider a circle with a radius of 6 units. A chord is drawn in this circle, dividing the circle into two segments. If the distance from the center of the circle to the chord is 4 units, what is the length of the chord?

To solve this problem, you can visualize the situation using a right triangle. The distance from the center of the circle to the chord is one leg of the triangle, the radius of the circle is the hypotenuse, and half the length of the chord is the other leg.

Let the length of the chord be denoted as $L$. By applying the Pythagorean theorem, you can express this relationship as:

$$ r^2 = d^2 + igg(\frac{L}{2}\bigg)^2 $$

where:

- $r$ is the radius of the circle (6 units),

- $d$ is the distance from the center of the circle to the chord (4 units).