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?
5
8
11
15
19
5
8
11
15
19
- Attachments
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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
