Question

In a circle of radius 17 cm, if a chord is at a distance of 8 cm from the centre of the circle, then the length of the chord is:
1. 24 cm
2. 28 cm
3. 30 cm
4. 20 cm

Answer 1

Correct Answer - Option 3 : 30 cm

Given:

The radius of the circle = 17 cm

The distance of a chord from the center = 8 cm

Concept used:

The shortest distance from the center to a chord bisects the chord

Detailed solution:

Let the length of the chord be 2x cm, then

Half of the length of the chord = x cm

Radius, the distance of chord from the center and half of the chord form a right-angled triangle, where

The hypotenuse is Radius i.e 17 cm

Base/Height is the half of the chord or the distance of the chord from the center i.e 8 cm / x cm

By Pythagoras theorem

Hypotenuse² = Base² + Height²

⇒ 17² = x² + 8²

⇒ 289 = x² + 64

⇒ x = √ 225

⇒ x = 15 cm

∴ The length of the chord is 30 cm