6)Equilateral triangle ABC is inscribed in a circle.If length of the arc ABC is 24,what is approximate diameter of the circle?

a 5 b 8 c 11 d 15 e19.
Oa 11

How to do this Ron?

here we have to consider two arcs,one is arc BAO and other is BOC (assuming centre of circle O)

then equation is 2*(120/360)*2*(22/7)*r=24

where r=radius of circle and 120 is the angle subtended by the arc at centre.

after calculation 2r=11.45which is approx 11

ok.

first comment: this problem is absolutely perfect for estimation. the answer choices are extremely spread out, so, if you don't clearly know how to solve the problem, just draw a decent picture and take your best guess.

in your diagram, the arc ABC should be two-thirds of the circle's circumference. therefore, one-third of the circumference (arc AB, or arc BC) is 12. if you've drawn a good picture, then, if you imagine straightening out that 12, it's awfully close to the diameter of the circle. therefore, you'd go with choice c.

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the real way to do the problem:
two-thirds of the circle's circumference is 24.
therefore, the circle's circumference is 36.
36 = pi * diameter
diameter = 36 / pi
= 36 / (a lil more than 3)
= a lil less than 12

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that works too.

in your diagram, you should probably trace out the arcs in color, rather than pointing to them with arrows; especially for larger arcs, it's unclear exactly where the arrow is pointing. (you can't really point at two-thirds of a whole circle - i.e., a 240° arc - with a single arrow, cool colors notwithstanding.)[/list]