Question

Consider the below figure where the diameter AB bisects the chord PQ at the point R. If BR = 4 cm, then what is the radius of the circle?

• A. 10

Answer 1

The correct option is A 10
Let $r$ be the radius of the circle.

We know that $OQ=OB=r$ and $OR=r-4(\because BR=4\text{cm})$
We also know that if the line segment drawn from the centre of a circle to a chord bisects the chord, then it is perpendicular to that chord.
Thus, $△ORQ$ is right-angled.
Using Pythagoras' theorem, we have
$\therefore O{Q}^2=Q{R}^2+R{O}^2.$
$\Rightarrow r^2=64+(r-4{)}^2$
$\Rightarrow r^2=64+r^2+16-8r$
$\Rightarrow 8r=80$
$\Rightarrow r=10\text{cm}$