In the figure above, equilateral triangle ABC

[Guest]

In the figure above, equilateral triangle ABC is inscribed in a circle. If the lenge of arc ABC is 24 what is the approximate diameter of the circle?

5
8
11*
15
19

[themarkac]

Here is how I solved it. I'm not sure if I did it correctly and I got 11.

An equilateral triangle has 3 equal 60 degree angles

60 degrees are the inscribed angles and the inscribed angles are 1/2 of the central angle. So each angle corresponds to an arc of 1/3 the diameter or a 120 degree central angles. If the arcs of the equilateral triangle add up to 24, then that means that it equals 2/3 of the triangle. so each arc is equal to 12 and the perimeter equals 36.

3.14 * X = 36

~ 11

Not sure if I did that correctly.

[RonPurewal]

search before you post
http://www.manhattangmat.com/forums/co- ... t2660.html

let's not re-invent the wheel here, people
thanks

[zarak_khan]

Thanks, Ron!

[RonPurewal]

Thanks, Ron!

sure