Question

If $\text{OM}=\text{ON}=4$ units, $\text{OP}=5$ units, then $\text{PQ}$ and $\text{RS}$ will be

• A. $8$ units, $8$ units
• B. $6$ units, $6$ units
• C. $5$ units, $8$ units
• D. $6$ units, $5$ units

Answer 1

The correct option is B $6$ units, $6$ units

Given that,
$\text{OM}=\text{ON}=4$ units
$\text{OP}=\text{OS}$
$=5$ units
$=$ Radius of the circle

From Pythagorus theorem, in the right angle triangle $\text{OMP}$
${\text{OM}}^2+{\text{MP}}^2={\text{OP}}^2$
$4^2+{\text{MP}}^2=5^2$
${\text{MP}}^2=5^2-4^2$
$=9=3^2$
$\text{MP}=3$ units

$\text{MP}$ is the mid point of $\text{PQ}$,
So, $\text{PQ}=2\times 3$
$=6$ units
Now, it is given that both chords are at same distances from the centre $\text{O}$.

Thus, $\text{PQ}=\text{RS}=6$ units