Question

Two chords, PQ and RS, are equal in length and are at a distance of 12 cm from the center of a circle. If the radius is 20 cm, what is the length of PQ?

• A. 16 cm
• B. 24 cm
• C. 32 cm
• D. 40 cm

Answer 1

Answer:

C. 32 cm

For a chord of a circle:

$\text{Half chord length}=\sqrt{r^2-d^2}$

where:

• Radius (r = 20) cm

• Distance of chord from center (d = 12) cm

$\frac{PQ}{2}=\sqrt{20^2-12^2}$

$=\sqrt{400-144}$

$=\sqrt{256}=16$

Therefore,

$PQ=2\times16=32cm$