Question

The radii of two intersecting circles are 17 cm and 25 cm. If the length of the common chord is 30 cm, find the distance between their centres.

Answer 1

Given:

Radii: r₁ = 17 cm, r₂ = 25 cm

Common chord length = 30 cm, so half-chord = 15 cm

Step-wise calculation:

1. Let the centres be O₁ and O₂ and let M be the midpoint of the common chord.

O₁M and O₂M are perpendicular to the chord and O₁M + O₂M = distance O₁O₂ = d.

2. Half-chord

`AM = 30/2` 

AM = 15 cm

3. By right triangles:

`O_1M = sqrt(r_1^2 - 15^2)`

= `sqrt(17^2 - 15^2)`

= `sqrt(289 - 225)`

= `sqrt(64)`

= 8 cm

`O_2M = sqrt(r_2^2 - 15^2)`

= `sqrt(25^2 - 15^2)`

= `sqrt(625 - 225)`

= `sqrt(400)`

= 20 cm

4. Therefore, d = O₁M + O₂M

= 8 + 20

= 28 cm

The distance between the centres is 28 cm.