Question

Two parallel chords are drawn in a circle of radius 15 cm. The length of one chord is 18 cm and the distance between the two chords is 21 cm. Find the length of another chord.

Answer 1

Given:

Radius = 15 cm

One chord = 18 cm

Distance between the two parallel chords = 21 cm

Step-wise calculation:

1. Half of the given chord

= `18/2`

= 9 cm

2. Distance from centre to that chord:

`d_1 = sqrt(R^2 - 9^2)`

= `sqrt(15^2 - 9^2)`

= `sqrt(225 - 81)`

= `sqrt(144)`

= 12 cm

3. Let the other chord have half-length x.

So, its distance from centre is `d_2 = sqrt(15^2 - x^2)`.

4. The chords must lie on opposite sides of the centre same-side placement would force an impossible distance.

So, d₁ + d₂ = 21.

Thus, `12 + sqrt(225 - x^2) = 21`.

5. `sqrt(225 - x^2) = 9`

⇒ 225 – x² = 81 

⇒ x² = 144

⇒ x = 12

6. Full length of the other chord

= 2x

= 24 cm