Question

The length of a chord is 30 cm and it is at a distance of 8 cm from the centre of the circle. Find the radius.

Answer 1

Given:

• The length of the chord is 30 cm, so half the length of the chord is:
  `30/2 = 15` cm
• The distance from the center of the circle to the chord is 8 cm.

Let r be the radius of the circle.

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

1. The radius of the circle (hypotenuse) = r,
2. The distance from the center of the circle to the chord (one leg) = 8 cm,
3. Half the length of the chord (the other leg) = 15 cm.

Using the Pythagorean theorem:

r² = (distance from center to chord)² + (half of the chord length)² 

Substitute the values:

r² = 8² + 15²

r² = 64 + 225

r² = 289

`r = sqrt(289) = 17` cm

Thus, the radius of the circle is 17 cm.