iran-konkur 2021 Q153

iran-konkur · Other · konkur-riazi_1400_specialized Circles Area and Geometric Measurement Involving Circles
153. According to the figure below, rectangle $ABCD$ is circumscribed about a circle with radius 3, and the circumference is $M\widehat{B}N = 120°$. What is the area of quadrilateral $OMNC$?
[Figure: Rectangle ABCD with inscribed circle centered at O, points M on AB and N inside, shaded region OMNC]
  • [(1)] $\dfrac{27\sqrt{3}}{4}$
  • [(2)] $\dfrac{9\sqrt{3}}{2}$
  • [(3)] $\dfrac{27\sqrt{3}}{2}$
  • [(4)] $9\sqrt{3}$

\textbf{153.} According to the figure below, rectangle $ABCD$ is circumscribed about a circle with radius 3, and the circumference is $M\widehat{B}N = 120°$. What is the area of quadrilateral $OMNC$?

\textit{[Figure: Rectangle ABCD with inscribed circle centered at O, points M on AB and N inside, shaded region OMNC]}

\begin{itemize}
    \item[(1)] $\dfrac{27\sqrt{3}}{4}$
    \item[(2)] $\dfrac{9\sqrt{3}}{2}$
    \item[(3)] $\dfrac{27\sqrt{3}}{2}$
    \item[(4)] $9\sqrt{3}$
\end{itemize}

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