Distance from Center to Chord in a Circle

Consider a circle with a center at point O located at the origin (0, 0) and a radius of 10 units. A chord AB of this circle is drawn perpendicular to the radius OC, where point C is on the circumference of the circle at coordinates (0, 10). If the length of chord AB is 12 units, what is the distance from the center O to the chord AB?

Use the properties of circles and right triangles to solve this problem.