Question

$AB$ and $CD$ are two parallel chords of length $8$ cm and $6$ cm respectively. If they are $1$ cm apart and lie on the same side of the centre of the circle, find the radius of the circle.

• A. $4$ cm
• B. $5$ cm
• C. $6$ cm
• D. $8$ cm

Answer 1

The correct option is B $5$ cm

Given,
$AB=8cm$
$CD=6cm$
$PQ=1cm$
Let radius of the circle be $r$
Therefore,
$OA=OC=r$
We know that the perpendicular dripped from the centre of the circle on the chord bisects the chord.
Therefore,
$CQ=QD=3cm$
$AP=PB=4cm$
Let $OP=x$
$=>OQ=x+1$
Now,
$O{A}^2=O{P}^2+A{P}^2$
$=>r^2=x^2+4^2$
$=>r^2=x^2+16$ (i)
$O{C}^2+O{Q}^2+C{Q}^2$
$=>r^2=(x+1{)}^2+3^2$
$=>r^2=x^2+2x+1+9$
$=>x^2+16=x^2+2x+1+9$ (from (i)
$=>2x=6$
$=>x=3$
Therefore,
$r^2=3^2+16$
$=>r^2=9+16$
$=>r^2=25$
$=>r=5cm$