Distance from Circle Center to Chord

A circle has a radius of 10 units. A chord within this circle is 12 units long. To find the distance from the center of the circle to the chord, we can use the formula that relates the radius of the circle, the distance from the center to the chord, and half the length of the chord.

If we let the distance from the center to the chord be denoted as $d$, we can express this relationship as:

$$r^2 = d^2 + m^2$$

where $r$ is the radius of the circle and $m$ is half the length of the chord. What is the value of $d$?