In the figure below, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?
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diameter of the circle? (GMAT Prep 2)
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Equilateral Triangle, AB = BC = CA, So, for the circle Arc AB = Arc BC = Arc CA
Arc ABC = Arc AB + Arc BC = 24. Thus, Arc Arc AB = 12 = Arc BC = Arc CA
So, perimeter of the circle = Arc AB + Arc BC + Arc CA = 3* 12 = 36 (as all Arc are same)
2*pie* radius = 36
=> radius = 36/(2*pie) = 5.73 approx
IMO 5
Arc ABC = Arc AB + Arc BC = 24. Thus, Arc Arc AB = 12 = Arc BC = Arc CA
So, perimeter of the circle = Arc AB + Arc BC + Arc CA = 3* 12 = 36 (as all Arc are same)
2*pie* radius = 36
=> radius = 36/(2*pie) = 5.73 approx
IMO 5
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As triangle ABC is equilateral, arc ABC is 2/3 of the circumference of the circle.alex.gellatly wrote:In the figure below, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?
Hence, circumference of the circle = 24*3/2 = 36
Hence, diameter of the circle = 36/Ï€ = Slightly less than 36/3 â‰ˆ 11
The correct answer is C.
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Right solution. However question asked for diameter.shovan85 wrote:Equilateral Triangle, AB = BC = CA, So, for the circle Arc AB = Arc BC = Arc CA
Arc ABC = Arc AB + Arc BC = 24. Thus, Arc Arc AB = 12 = Arc BC = Arc CA
So, perimeter of the circle = Arc AB + Arc BC + Arc CA = 3* 12 = 36 (as all Arc are same)
2*pie* radius = 36
=> radius = 36/(2*pie) = 5.73 approx
IMO 5