Question

A chord 16 cm long is 6 cm away from the centre of the circle. Then the chord of length 8 cm is ___ cm away from the centre.

• A. $\sqrt{21}$ cm
• B. $2\sqrt{21}$ cm
• C. $3\sqrt{21}$ cm
• D. $4\sqrt{21}$ cm

Answer 1

The correct option is B

$2\sqrt{21}$ cm

Given, a chord 16 cm long is 6 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,

$(\frac{1}{2}\times 16{)}^2=r^2-6^2$

$⟹64=r^2-36$

$⟹r^2=100$

$⟹r=10$ cm

Let the chord of length 8 cm be $x$ cm away from the centre.

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

$⟹16={10}^2-x^2$

$⟹x^2=84$

$⟹x=\sqrt{84}$

$⟹x=2\sqrt{21}$ cm