Question

O is the centre of the circle whose radius is 17 cm. Find the distance of the chord from the centre if the length of the chord is 30 cm.

• A. 7 cm
• B. 14 cm
• C. 11 cm
• D. 8 cm

Answer 1

The correct option is D 8 cm


PO is the radius of the circle
$\therefore PO=17cm$.
Given, the length of the chord $PQ=30cm$.
The perpendicular from the centre of the circle to the chord bisects the chord.
$\therefore PM=MQ=15cm$.
Using Pythagoras theorem in $\Delta POM$,
we get,
$P{O}^2=P{M}^2+M{O}^2$
${17}^2={15}^2+M{O}^2$
$\Rightarrow M{O}^2=289-225=64$
$\Rightarrow MO=8cm.$