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If a diameter of a circle is 82 cm in length and a chord is 80 cm in length, how far is the chord from the center?​

Sagot :

Nzmidn

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

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