Question

The diameter of a circle is 82 cm and the length of a chord is 80 cm. Calculate the distance of the chord from the centre of the circle.

Answer 1

Given:

• The diameter of the circle is 82 cm, so the radius r of the circle is:
  `r = "diameter"/2 = 82/2 = 41` cm
• The length of the chord is 80 cm, so half the length of the chord is:
  `80/2 = 40` cm

Let d be the distance from the center of the circle to the chord.

In this case, we have a right-angled triangle formed by:

1. The radius of the circle (hypotenuse) = 41 cm, 
2. The distance from the center of the circle to the chord (one leg) = d,
3. Half the length of the chord (the other leg) = 40 cm. 

Using the Pythagorean theorem:

r² = d² + (half of the chord length)²

Substitute the values:

41² = d² + 40²

1681 = d² + 1600

d² = 1681 – 1600 = 81

`d = sqrt(81) = 9` cm

Thus, the distance of the chord from the center of the circle is 9 cm.