Question

A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.

• A. 30 cm
• B. 24 cm
• C. 16 cm
• D. 18 cm

Answer 1

The correct option is C 16 cm

As per question given details:

a chord 12cm is 8cm distance from the centre of the circle.

Assume that centre of the circle be O and E The mid point of AB. AEO and BEO are both right angled triangle.

i.e $AE=\frac{12}{2}$and EO=8cm, so R the radius of the circle is

$\sqrt{\left[6^2+8^2\right]}=\sqrt{\left(36+64\right)}=\sqrt{100}=10cm$

Now the chord CD is 6cm from O. Let F be the mid point of CD. CFO and DFO are both right angled triangle. $FO=6cm$ and $CO=DO=10cm$, so

$CF=DF=\sqrt{\left[{10}^2-6^2\right]}=\sqrt{100-36}=\sqrt{64}=8cm$

So, as per solution

$D=2\times 8=16cm$