Question

A chord of length $12$ cm is at a distance of $8$ cm from the center of a circle. Find the length of a chord of the same circle which is at a distance $6$ cm from the center.

• A. $32$ cm
• B. $20$ cm
• C. $16$ cm
• D. $18$ cm

Answer 1

The correct option is C $16$ cm

In
a circle, the perpendicular bisector from the centre to the mid point of the
chord, forms a right angled triangle as shown in the figure.
Now,
$=>{OA}^2={OM}^2+{MA}^2$
$=>{OA}^2=8^2+6^2$ (Since,
MA is half of the chord AB )
$=>OA=Radius=10cm$
Let the other chord be PQ.
Similarly,
$=>{OP}^2={ON}^2+{NP}^2$
$=>{10}^2=6^2+{NP}^2$ (Since, NP is half of the chord PQ )
$=>NP=8cm$
SO, $PQ=2\times NP=16cm$