Question

In the figure above (Not to scale) PQ is a tangent drawn to the circle with centre O at P and QR = RO If $PQ=3\sqrt{3}$ cm and ORQ is a line segment then find the radius of the circle (in cm)

• A. $\sqrt{3}$
• B. $2\sqrt{3}$
• C. $3$
• D. $3\sqrt{3}$

Answer 1

The correct option is C $3$

$OP=OR=radius$

$OR=QR$ (given)

WKT

$OP\perp PQ$

$⟹O{Q}^2=O{P}^2+P{Q}^2$

$(OR+RQ{)}^2=r^2+(3\sqrt{3}{)}^2$

$4r^2–r^2=27⟹r^2=9⟹r=3cm$