Question

In a circle of radius 13 cm, two parallel chords of lengths 24 cm and 10 cm are drawn. Find the distance between the chords, if both the chords are

1. on the same side of the centre.
2. on the opposite side of the centre.

Answer 1

Given: A circle of radius 13 cm with two parallel chords of lengths 24 cm and 10 cm.

Find the distance between the chords when

1. they lie on the same side of the centre.
2. they lie on opposite sides of the centre.

Step-wise calculation:

1. Half-lengths of the chords:

For the 24 cm chord: `24/2` = 12 cm.

For the 10 cm chord: `10/2` = 5 cm.

2. Distance from centre to each chord `("use"  OM = sqrt(r^2 - ("half‑chord")^2))`:

Distance to 24 cm chord:

`sqrt(13^2 - 12^2)`

= `sqrt(169 - 144)`

= `sqrt(25)`

= 5 cm

Distance to 10 cm chord:

= `sqrt(13^2 - 5^2)` 

= `sqrt(169 - 25)`

= `sqrt(144)`

= 12 cm

3. Compute distance between chords:

If both chords are on the same side of the centre: the distance between them is the absolute difference of their centre distances

= |12 − 5|

= 7 cm

If they are on opposite sides of the centre: the distance between them is the sum of their centre distances

= 12 + 5

= 17 cm

1. Same side of centre: 7 cm. 
2. Opposite sides of centre: 17 cm.