Question

The figure is a circle with center $O$ and diameter $10$ cm, $PQ=1$ cm. Find the length of $RS$.

• A. $6$ cm
• B. $4$ cm
• C. $5$ cm
• D. $3$ cm

Answer 1

Answer: (A)

$6$ cm

Diameter of circle $=10$ cm

Radius of circle $=r=\frac{10}{2}=5$ cm

Thus $OQ=OR=r=5$ cm

$\Rightarrow OQ=OP+PQ$

$\Rightarrow 5=OP+1$

$\Rightarrow OP=4$ cm

Applying pythagoras theorem in $△ORP$, we have

${\left(OR\right)}^2={\left(RP\right)}^2+{\left(PO\right)}^2\Rightarrow {\left(5\right)}^2={\left(RP\right)}^2+{\left(4\right)}^2\Rightarrow {\left(RP\right)}^2=9\Rightarrow RP=3$

Perpendicluar from the centre to a chord of circle bisects the chord.

Therefore, $RS=2RP$

$\Rightarrow RS=2\times 3=6$ cm

Option A is correct.