Question

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD = 32 cm and EB = 4 cm, then find the radius of the circle.
[4 Marks]

Answer 1

[ 1 Mark]

Let $OE=x$ cm.
Given, $EB=4$ cm.
Then, the radius of the circle will be $OB=OE+EB=(x+4)$ cm,
$\Rightarrow OD=(x+4)$ cm
[1 Mark]

Also, it is given that diameter AB bisects the chord CD at point E. Hence, $CE=ED=\frac{32}{2}=16cm.$
We know that if a line drawn from the centre of a circle bisects the chord, then the line is perpendicular to that chord.
i.e., $OE\perp ED$
[1 Mark]

Then, by using Pythagoras' theorem in $\Delta OED$, we get,
$(4+x{)}^2=x^2+{16}^2$
$\Rightarrow 16+x^2+8x=x^2+256$
$\Rightarrow x=30$
$\therefore \text{Radius of circle}=x+4=30+4=34cm$
[1 Mark]