OpenSAT

Draw a diagram of the circle, the chord, and the radius from the center of the circle to the midpoint of the chord. This radius bisects the chord, creating two right triangles. The hypotenuse of each triangle is a radius of the circle (6 units), and one leg of each triangle is half the chord (4 units). We can use the Pythagorean Theorem to find the other leg (the distance from the center to the chord): $6^2 = 4^2 + d^2$, where $d$ is the distance from the center of the circle to the chord. Solving for $d$, we find $d = \sqrt{6^2 - 4^2} = \sqrt{20} = 2\sqrt{5}$. Since the distance from the center to the chord is half of this distance, the distance from the center of the circle to the chord is $\sqrt{5}$ units.