An equilateral triangle ABC is inscribed in a circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?
A) 5
B) 8
C) 11
D) 15
E) 19
I thought I had this question easily figured out, but it's not any of the answer choices, so I'm pretty certain I'm doing something wrong
. ...so your explanations are appreciated and I'm sure I'm overlooking something pretty elementary.
My logic is this:
Equilateral triangle = 60 degrees for all 3 angles. So the arc ABC must be sitting at 60 degrees. But it is on the outer part of the circle, so 60 * 2 will bring us to the center = 120 degrees. 120 / 360 means the arc is 1/3 of the circle. We know the arc is 24, so 24 * 3 is 72.
The circumference of the circle is pi * d so the diameter is 72 / pi which is approximately equal to 23.
Please tell me where i'm leading myself astray.
A) 5
B) 8
C) 11
D) 15
E) 19
I thought I had this question easily figured out, but it's not any of the answer choices, so I'm pretty certain I'm doing something wrong
. ...so your explanations are appreciated and I'm sure I'm overlooking something pretty elementary.My logic is this:
Equilateral triangle = 60 degrees for all 3 angles. So the arc ABC must be sitting at 60 degrees. But it is on the outer part of the circle, so 60 * 2 will bring us to the center = 120 degrees. 120 / 360 means the arc is 1/3 of the circle. We know the arc is 24, so 24 * 3 is 72.
The circumference of the circle is pi * d so the diameter is 72 / pi which is approximately equal to 23.
Please tell me where i'm leading myself astray.
