Question

In the given figure, PQ and PR are two tangents drawn from an external point P to a circle with centre 'O'. If OQ = 3 cm and PS = 2cm then, find the perimeter (in cm) of quadrilateral PQOR.

• A. 12
• B. 14
• C. 10
• D. 16

Answer 1

The correct option is B 14

$OQ$ = $OR$ = 3 cm
$PO$ = $PS$ + $OS$ = 2 + 3 = 5 cm
By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact.
We know that PQ and PR are tangents, hence
$\angle$$PQO$ = $\angle$$PRO$ = ${90}^{\circ }$

Now, applying pythagoras theorem in right $△$ OQP
$P{O}^2=P{Q}^2+O{Q}^2$
$P{Q}^2=5^2-3^2$
$PQ$ = 4 cm

Thus $PQ$ = $PR$ = 4cm ( By Theorem- Tangents drawn from an external point to a circle are equal in length)

Perimeter of quadrilateral $PQOR$ is sum of all sides

= $PQ$ + $PR$ + $OQ$ + $OR$

= 4 + 4 + 3 + 3

= 14 cm