The chord subtracts the arc 90 degrees, and is equal to 16. Find the distance from the center of the circle.

From point O, the center of the circle, draw the radii to the edges of the chord AB.

Since the chord AB contracts the arc at 90, the central angle AOB is equal to the degree measure of the arc AB.

Angle AOB = 90.

Then the triangle AOB is rectangular and isosceles, since OA = OB = R.

Let’s draw the height OH to the base AB of triangle AOB.

The height of OH is also the median of the triangle, then AH = BH = AB / 2 = 16/2 = 8 cm.

The AON triangle is also rectangular and isosceles, then AH = OH = 8 cm.

Answer: The distance from point O to chord AB is 8 cm.