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 $OM=ON=2$ 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

Given- $AB$ and $CD$ are two chords of a circle with centre $O$.

$OM\perp AB$ and $ON\perp CD$

$AM=AN=4.5$ cm

$OM=ON=2$ cm

Solution-

$AM=AN=4.5$ cm

$\therefore AB=AM+AN=(4.5+4.5)$ cm $=9$ cm

$OM$ and $ON$ are the perpendicular distances of $AB$ and $CD$ respectively.

Since $OM\perp AB$ and $ON\perp CD$

Now $OM=ON=2$ cm

$\therefore AB$ and $CD$ are equidistant from $O$.

$\therefore AB=CD$

Since chords of a circle, which are equidistant from the centre of the same circle are equal in length.

$\therefore AB=CD=9$ cm