Question

In the given figure, CD is a chord 3 cm away from the centre of the circle. What will be the length of CD if the radius of the circle is 5 cm?

• A. 6 cm
• B. 8 cm
• C. 4 cm
• D. 7 cm

Answer 1

The correct option is B 8 cm

Join OB to get the right angled triangle OPD.
Note that OB = 5 cm as it is the radius of the circle.

Since a perpendicular from the centre of a circle to a chord bisects the chord, we have
$AP=PB=4\text{cm}.$
$⟹AB=4+4=8\text{cm}$

Consider $△OPB.$
Using Pythagoras' theorem,
$O{B}^2=O{P}^2+P{B}^2.$
$⟹O{P}^2=O{B}^2-P{B}^2$
$=5^2-4^2$
$=9{\text{cm}}^2$
$⟹OP=3\text{cm}$
i.e., $OP=ON$

Chords that are equidistant from the centre of a circle are equal in measure.
$⟹CD=AB=8\text{cm}$