SSC CGL Model Paper 5

Question : 57 of 100

Marks: +1, -0

In the given figure, O is the centre of the circle and ∠AOD = 120°. If the radius of the circle is 'r unit', then find the sum of the areas On unit

^{2}

) of quadrilaterals AODP and OBQC.

Solution:

OQ=OB =OC=r

∠AOD = ∠BOC = 120°
∴ ∠BOQ = ∠COQ = 60°
Now, in ΔOSB,

\sin60°={SB}/{OB}=√3/2

⇒

SB={r√3}/2

∴

BC = 2SB = r √3

∴ Area of quadrilateral BOCQ,

=1/2×BC×OQ

=1/2×r√3×r={r^2√3}/2\Unit^2

∴ Area of both the quadrilaterals

=2({r^2√3}/2)= √3 r^2\Unit^2

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