talaangoshtari wrote:A circle is inscribed in an equilateral triangle, such that the two figures touch at exactly 3 points, one on each side of the triangle. Which of the following is closest to the percent of the area of the triangle that lies within the circle?
(A) 50%
(B) 55%
(C) 60%
(D) 65%
(E) 70%
The equilateral triangle can be divided into six 30-60-90 triangles, as follows:
Area of the circle = πr² = π(1²) ≈ 3.
Area of ∆ABC = (1/2)(AB)(BD) = (1/2)(2√3)(3) = 3√3 ≈ (3)(1.7) ≈ 5.
(circle)/(triangle) * 100 = (3/5)(100) = 60%.
The correct answer is
C.
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