In a circle, the perpendicular bisector of a chord passes through the center of the circle. Since the chord is 10 cm from the center of the circle, we can draw the perpendicular bisector of the chord that passes through the center of the circle, as shown in the diagram below:
O
/ \
/ \
/ \
/ \
/ \
/ \
A-----------------B
10 cm
Since the perpendicular bisector passes through the center of the circle, we can draw a radius of length 12 cm that intersects the perpendicular bisector at a right angle. This creates a right triangle OAB, where OA = OB = 12 cm and AB = 10 cm/2 = 5 cm.
Using the Pythagorean theorem, we can find the length of the chord:
AB^2 + OB^2 = OA^2
5^2 + 12^2 = 144 + 25
169 = 169
Therefore, the length of the chord is the square root of 169, which is 13 cm. So, the length of the chord is 13 cm.