In the figure above, equilateral triangle ABC is inscribed
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- Jay@ManhattanReview
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Given that ∆ABC is an equilateral triangle, arc AB, arc BC and arc CA are equal. We have arc ABC = (arc AB + arc BC + arc CA) - arc CA.
=> arc ABC = 24 = Circumference of the circle - 1/3 of Circumference of the circle = 2/3 of Circumference of the circle
=> Circumference of the circle = 24 * 3/2 = 36
=> 36 = πD, where D = diamater of the circle
=> D = appx. 11.
The correct answer: C
Hope this helps!
-Jay
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Let center be denoted as O. Draw lines OA & OC. Now Angle ABC=60(equilateral triangle) & hence Angle AOC=120.
Length of the arc ABC = (x /360) * circumference, where x = 240 (ext. angle of O)
\(24 = \frac{240}{360}\cdot 2 \pi \cdot r\)
\(D = \frac{36\cdot 7}{22} \approx 11.14 \approx 11 \Rightarrow\) __C__.
Length of the arc ABC = (x /360) * circumference, where x = 240 (ext. angle of O)
\(24 = \frac{240}{360}\cdot 2 \pi \cdot r\)
\(D = \frac{36\cdot 7}{22} \approx 11.14 \approx 11 \Rightarrow\) __C__.
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- Scott@TargetTestPrep
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We are given that the length of arc ABC is equal to 24. Since arc AB, BC, and CA each represent 1/3 of the circumference, arc ABC represents 2/3 of the circumference. Thus, we can create the following equation.
2/3(circumference) = 24
2/3(Ï€d) = 24
Ï€d = 24 x 3/2
Ï€d = 36
d = 36/Ï€
d ≈ 11
Answer: C
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The equilateral triangle cuts the circle in 3 equal arcs.
Arc ABC travels the length of 2 of those arcs .
So, each arc must have length 12, which means the TOTAL CIRCUMFERENCE = (3)(12) = 36
Now, we'll use the formula: CIRCUMFERENCE = (Ï€)(diameter)
So, 36 ≈ (3.14)(diameter)
This means that: diameter = 36/3.14
IMPORTANT: We need not perform any long division here. Notice that the answer choices are nicely spread apart. So, we can ESTIMATE.
We know that 36/3 = 12
Since 3.14 is a bit bigger than 3, we know that 36/3.14 will be a bit smaller than 12.
Answer choice C is a bit smaller than 12, so it must be the correct answer.
Cheers,
Brent