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Question: Answered & Verified by Expert
Among all cyclic quadrilaterals inscribed in a circle of radius $\mathrm{R}$ with one of its angles equal to $120^{\circ}$. Consider the one with maximum possible area. Its area is-
MathematicsCircleKVPYKVPY 2010 (SB/SX)
Options:
  • A $\sqrt{2} \mathbb{R}^{2}$
  • B $\sqrt{3} \mathrm{R}^{2}$
  • C $2 \mathbb{R}^{2}$
  • D $2 \sqrt{3} \mathrm{R}^{2}$
Solution:
2232 Upvotes Verified Answer
The correct answer is: $\sqrt{3} \mathrm{R}^{2}$


$\mathrm{A}=2 \times \frac{1}{2} \times \sqrt{3} \mathrm{R} \times \mathrm{R}=\sqrt{3} \mathrm{R}^{2}$

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