Question

$O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM\perp AB$ and $ON\perp CD$. If $OM=ON=3$ cm and $AM=BM=4.5$ cm, then $CD$ is equal to

• A. $8$ cm
• B. $9$ cm
• C. $10$ cm
• D. None of these

Answer 1

The correct option is B $9$ cm

$In△OMB$

$O{B}^2=r^2=O{M}^2+M{B}^2$

$r=\sqrt{3^2+{4.5}^2}=\sqrt{29.25}$

Since $ON\perp CD$

$CN=ND$

$In△OND$

$O{D}^2=r^2=O{N}^2+N{D}^2$

$29.35=9+N{D}^2$

$ND=4.5cm$

$CD=2ND=2\times 4.5=9cm$