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?

Solution (By Examveda Team)

In ΔODS
1 unit → 9 cm
√3 units → 9√3 cm
So, D is the mid point of SR
So DS = 9√3
SR = 18√3
In ΔPCO
√3 units → 9 unit
1 unit → $$\frac{9}{{\sqrt 3 }}$$ = 3√3 = PC
⇒ PQ = 6√3
Sum of pair of 2 opposite side is equal to sum of pair of other two opposite sides.
So, PQ + SR = SP + QR
Perimeter = 2(18√3 + 6√3) = 48√3