The radius of a circle is 8 cm and the length of one of it's chord is 12 cm find the distance of the chord from the center.

Draw a radius perpendicular to the chord. Draw a radius to the end of the chord.

Now you have a right triangle where

x^2+6^2 = 8^2

To find the distance of the chord from the center, we can use a theorem called the perpendicular bisector theorem, which states that a line segment that is perpendicular to a chord and bisects it, also passes through the center of the circle.

Here's how we can solve the problem step by step:

1. Draw a circle with a radius of 8 cm.
2. Draw a chord with a length of 12 cm.
3. To find the distance of the chord from the center, we need to find the perpendicular bisector of the chord.
4. Draw a line segment from the midpoint of the chord to the center of the circle. This segment will be perpendicular to the chord, as the perpendicular bisector theorem states.
5. Let's call the point where the perpendicular bisector intersects the chord as "P". Also, let's call the point where it intersects the circle as "Q", and the center of the circle as "O".
6. The perpendicular bisector will not only split the chord into two equal halves, but it will also split the line segment from the center to point "Q" (the radius) into two equal halves.
7. Since the radius is 8 cm, the length from the center to point "P" will be half of that, which is 4 cm. Hence, the distance of the chord from the center is 4 cm.