SOLUTION:
Since the diameter of the circle is 82 cm, its radius is 41 cm.
Now, connect the center of the circle to the starting/ending point of the chord. (note that the line formed here is the radius of the circle)
Once again, connect the center of the circle to the midpoint of the chord, then the distance between the starting/ending point and midpoint of the chord is 80/2 = 40 cm.
Since the lines we connected are perpendicular, the formed figure is a right triangle
By Pythagorean Theorem,
a² + b² = c²
In this case, we have a = 40 cm, b = distance of the cord from the center, and c = 41.
Substituting,
40² + b² = 41²
1600 + b² = 1681
b² = 1681 - 1600
b² = 81
√b² = √81
b = 9 cm
Therefore, the distance between the chord from the center is 9 cm.
ANSWER:
9 cm
