Question

The diameter of a circle is 50 cm. A chord is at a distance of 7 cm from the centre of the circle. Find the length of the chord.

Answer 1

Given:

• The diameter of the circle is 50 cm, so the radius r of the circle is:
  `r = "diameter"/2 = 50/2 = 25` cm
• The distance from the center of the circle to the chord is 7 cm.

Let the length of the chord be 2x. The perpendicular from the center of the circle to the chord bisects the chord, so each half of the chord is x.

Now, we have a right-angled triangle formed by:

1. The radius of the circle (hypotenuse) = 25 cm, 
2. The distance from the center of the circle to the chord (one leg) = 7 cm, 
3. Half the length of the chord (the other leg) = x.

Using the Pythagorean theorem:

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

Substitute the values:

25² = 7² + x²

625 = 49 + x²

x² = 625 – 49 = 576

`x = sqrt(576) = 24  cm`

Thus, the total length of the chord is:

Length of the chord = 2x = 2 × 24 = 48 cm

So, the length of the chord is 48 cm.