Two parallel chords are drawn in a circle of radius 25 cm. The distance between the two chords is 27 cm. If the length of one chord is 48 cm, then length of the other chord is equal to:

Given:

Radius of the circle = 25 cm.

Distance between the two chords = 27 cm.

Length of one chord = 48 cm.

Formula Used:

For a chord of length 2l at a distance d from the center in a circle of radius R :

\(l = \sqrt{R^2 - d^2}\)

Calculation:

Let the two chords be AB and CD with AB = 48 cm and CD = x cm.

Distance of AB from the center OM = \(d_1\)

Distance of CD from the center ON = \(d_2\)

Given, \(d_1\) + \(d_2\) = 27 cm

Half of AB = 24 cm

Half of CD = x/2 cm

Using the formula for chord length:

24 = \(\sqrt{25^2 - d_1^2}\)

x/2 = \(\sqrt{25^2 - d_2^2}\)

Solving for \(d_1\) :

\(24 = \sqrt{625 - d_1^2}\)

Squaring both sides:

⇒ 24² = 625 - \(d_1^2\)

⇒ 576 = 625 - \(d_1^2\)

⇒ \(d_1^2\) = 625 - 576

⇒ \(d_1^2\) = 49

⇒ \(d_1\) = 7 cm

Since \(d_1\) + \(d_2\) = 27 :

⇒ \(d_2\) = 27 - 7

⇒ \(d_2\) = 20 cm

Using \(d_2\) to find x:

\(x/2 = \sqrt{625 - 20^2}\)

⇒ x/2 = \( \sqrt{625 - 400}\)

⇒ x/2 = √225

⇒ x/2 = 15

⇒ x = 30 cm

The length of the other chord is 30 cm.