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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
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B
14
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C
10
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D
16
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Solution

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
PQO = PRO = 90

Now, applying pythagoras theorem in right OQP
PO2=PQ2+OQ2
PQ2=5232
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


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