In the given figure a circle touches the sides of the quadrilateral PQRS The radius of the circle is...........

Quantitative Aptitude ( CCS) Geometry

In the given figure, a circle touches the sides of the quadrilateral PQRS. The radius of the circle is 9 cm. ∠RSP = ∠SRQ = 60° and ∠PQR = ∠QPS = 120°. What is the perimeter (in cm) of the quadrilateral ?

36√3

24√3

48√3

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Explanation:

∠RSP = ∠SRO = 60 (Given)
∠PQR = ∠QPS = 120 (Given)
In a quadrilateral PMOK
∠MOK = 180 – 120 = 60
∠POM = ∠KOP = 30
OK = OM = 9 (Given)
In ?POM
tan?30=PM/9 ⇒PM=3√3=PK=MQ=QL