In an equilateral triangle of side 2\sqrt{3}\text{ cm}, a circle is inscribed touching the sides. What is the area of the remaining portion of the triangle ?
- A. (2\sqrt{3}-\pi)\text{ square cm}
- B. (3\sqrt{3}-\pi)\text{ square cm} ✓
- C. (4\sqrt{3}-2\pi)\text{ square cm}
- D. (4\sqrt{3}-\pi)\text{ square cm}
Correct Answer: B. (3\sqrt{3}-\pi)\text{ square cm}
Explanation
Area of equilateral triangle = \frac{\sqrt{3}}{4}(2\sqrt{3})^2 = 3\sqrt{3}. The inradius r = \frac{\text{side}}{2\sqrt{3}} = \frac{2\sqrt{3}}{2\sqrt{3}} = 1\text{ cm}. Area of the inscribed circle = \pi(1)^2 = \pi. The remaining area is (3\sqrt{3} - \pi)\text{ square cm}.
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