Question

$O$ is the centre of the circle having radius $5$ cm. $OM\perp$ chord $AB$. If $OM=4$ cm, then the length of the chord $AB$ is

• A. $6$ cm
• B. $5$ cm
• C. $8$ cm
• D. $10$ cm

Answer 1

The correct option is A $6$ cm

Radius, $OA=OB=5cm$
$OM=4cm$
Now,
$O{A}^2=A{M}^2+O{M}^2$
$=>5^2=A{M}^2+4^2$
$=>-A{M}^2=-25+16$
$=>A{M}^2=9$
$=>AM=3$
Now, we know that $\perp$ dropped from the centre of the circle to the chord bisect the chord.
Therefore,
$AB=AM+MB$
$=>AB=2AM$
$=>AB=2\times 3$
$=>AB=6cm$