Question

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.

• A. 6 cm
• B. 7 cm
• C. 8 cm
• D. 9 cm

Answer 1

The correct option is C 8 cm

AC is the radius of the circle
$\therefore AC=10cm$
The perpendicular from the centre of the circle to the chord bisects the chord.
$\therefore AD=DB=6cm$
Using Pythagoras theorem in $\Delta ACD$,
we get,
$A{C}^2=A{D}^2+C{D}^2$
${10}^2=6^2+C{D}^2$
$\Rightarrow C{D}^2=100-36=64$
$\Rightarrow CD=8cm$

Hence, the distance of the chord from the centre = CD = 8 cm.