Question

O 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 16 cm.

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

Answer 1

The correct option is A 6 cm

RO is the radius of the circle
$\therefore RO=10cm$.
The perpendicular from the centre of the circle to the chord bisects the chord.
$\therefore RM=MT=8cm$.
Using Pythagoras theorem in $\Delta ROM$,
we get,
$R{O}^2=R{M}^2+M{O}^2$
${10}^2=8^2+M{O}^2$
$\Rightarrow M{O}^2=100-64=36$
$\Rightarrow MO=6cm.$

Hence, the distance of the chord from the centre = MO = 6 cm.