What is the ratio of the area of the circle to the area of the rectangle?
Consider the following for the next two (02) items that follow:<br>In the following figure, a rectangle ABCD is inscribed in a circle of radius r. Given \angle DAE=30^{\circ} and \angle ACD=30^{\circ}.
- A. \frac{\pi}{\sqrt{2}}
- B. \frac{\pi}{\sqrt{3}} ✓
- C. \frac{2\pi}{\sqrt{3}}
- D. \frac{3\pi}{\sqrt{2}}
Correct Answer: B. \frac{\pi}{\sqrt{3}}
Explanation
In right \triangle ADC, the diagonal AC = 2r. Since \angle ACD = 30^{\circ}, AD = r and CD = r\sqrt{3}. The area of the rectangle is r^2\sqrt{3}. The ratio of the circle's area to the rectangle's area is \frac{\pi r^2}{r^2\sqrt{3}} = \frac{\pi}{\sqrt{3}}.
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