Question

From the given figure below, what are the length of the chords $\text{CD}$ and $\text{RS}$ if $\text{O'M}=\text{O'N},\text{OX}=\text{OY}$ and the length of $\text{AM}$ and $\text{PX}$ are $2$ units and $3$ units respectively.

• A. $\text{CD}=4$ units
  $\text{RS}=6$ units
• B. $\text{CD}=6$ units
  $\text{RS}=4$ units
• C. $\text{CD}=4$ units
  $\text{RS}=9$ units
• D. $\text{CD}=9$ units
  $\text{RS}=4$ units

Answer 1

The correct option is A $\text{CD}=4$ units

$\text{RS}=6$ units
Given that,
$\text{PX}=3$ units
$\text{AM}=2$ units
$\text{O'M}=\text{O'N}$
$\text{OX}=\text{OY}$

Let's consider the circle with center $\text{O'}$
Since, $\text{O'M}=\text{O'N}$
Hence, length of chords $\text{AB}$ and $\text{CD}$ will be the same,
i.e. $\text{AB}=\text{CD}$
Now,
$\text{AM}=\frac{\text{AB}}{2}$
so, $\text{AB}=2\times \text{AM}$
$=2\times 2$
$=4$ units
Therefore, $\text{CD}=4$ units

Let's consider the circle with center $\text{O}$
Since, $\text{OX}=\text{OY}$
Hence, length of chords $\text{PQ}$ and $\text{RS}$ will be the same,
i.e. $\text{PQ}=\text{RS}$
Now,
$\text{PX}=\frac{\text{PQ}}{2}$
so, $\text{PQ}=2\times \text{PX}$
$=2\times 3$
$=6$ units
Therefore, $\text{RS}=6$ units