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%
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talaangoshtari
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The equilateral triangle can be divided into six 30-60-90 triangles, as follows: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%
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.
To see how the figure above can be derived, check my second post here:
https://www.beatthegmat.com/circle-withi ... 90186.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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Student Review #3
