Question

The adjoining figure shows a circle with centre $O$ in which a diameter $AB$ bisects the chord $PQ$ at point $R$. If $PR=RQ=8$ cm and $RB=4$ cm, find the radius of the circle.

• A. $10$ cm
• B. $8$ cm
• C. $12$ cm
• D. $16$ cm

Answer 1

The correct option is A $10$ cm

$AB$ bisects chord $PQ$ at point $C$.
Therefore,
$PR=QR=8cm$
$RB=4cm$
Let, radius $OA=OB=r$
$OB=OR+RB$
$=>r=OR+4$
$=>OR=r-4$ (i)
Now,
$O{P}^2=O{R}^2+P{R}^2$
$=>r^2=(r-4{)}^2+8^2$ (using (i)
$=>r^2=r^2-8r+16+64$
$=>8r=80$
$=>r=10cm$
The radius of the circle is $10cm$