Question

A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?

• A. 12 cm
• B. 14 cm
• C. 16 cm
• D. 18 cm

Answer 1

The correct option is C

16 cm

Given, a chord 12 cm long is 8 cm away from the centre of the circle.

We know, in a circle, the square of half the length of a chord is the difference of the squares of the radius and the perpendicular distance of the chord from the centre of the circle.

Let the radius of the circle be $r$.

Then, we must have,

$(\frac{1}{2}\times 12{)}^2=r^2-8^2$

$⟹36+64=r^2$

$⟹r^2=100$

$⟹r=10$ cm

We shall now find the length of the chord which is 6 cm away from the centre.

Let the length of the chord which is 6 cm away from the centre be $l$ cm.

Then $(\frac{1}{2}\times l{)}^2=r^2-6^2$

$⟹(\frac{1}{2}\times l{)}^2={10}^2-6^2$

$⟹(\frac{1}{2}\times l{)}^2=64$

$⟹(\frac{1}{2}\times l)=8$

$⟹l=16$ cm