Question

In the given figure, a circle with centre O is inscribed in a quadrilateral PQRS in which $\angle S={90}^{\circ }$. If PQ = 9 cm, PS = 13 cm and QU = 3 cm, then the radius of the circle is

• A.
  $5cm$
• B.
  $6cm$
• C.
  $7cm$
• D.
  
  $7\sqrt{2}cm$
  

Answer 1

The correct option is C

$7cm$
Given: PQ = 9 cm, PS = 13 cm, QU = 3 cm

Here, PQ, QR, RS and PS are tangents to the circle at points T, U, V and W respectively.


Now, QT = QU = 3 cm
(Lengths of tangents drawn from an external point are equal)

Similarly,

$\Rightarrow PW=PT=9–3=6cm\Rightarrow SV=SW=13–6=7cm\text{Since, PS and SR are tangents.}\Rightarrow OW\perp PSandOV\perp SR\text{(Angle between a tangent and the}\text{radius of a circle is}{90}^{\circ })$

Thus, in quadrilateral OWSV, $\angle S=\angle W=\angle V={90}^{\circ }$

$\Rightarrow \angle WOV={90}^{\circ }$

$\therefore OWSVisasquare.\Rightarrow WS=SV=OW=OV=7cm$

Thus, the radius of circle with centre O is 7 cm.

Hence, the correct answer is option c.