Since the triangle is an equilateral triangle we can infer that the arcs AB, BC & AC are of same length. Using this arc ABC = 2/3 perimeter of triangle = 2(pi)r * 2/3
Given Arc ABC = 24.
This leads us to 24 = 2(pi)r * 2/3
=> r = 18/pi = 18/3.14 = approx (5.7)
Hence diameter = 2r = 11.4 (approx)
C is the closest one to this hence it is the right answer.
Triangle inscribed in circle
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asamaverick
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Testluv
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This should be: 24 = (2/3)*circumference of circle = (2/3)*2*pi*rUsing this arc ABC = 2/3 perimeter of triangle = 2(pi)r * 2/3
and we want 2r, so:
2r = 36/pi = approx. 11
Kaplan Teacher in Toronto
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ssuarezo
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Thank u guys,Testluv wrote:This should be: 24 = (2/3)*circumference of circle = (2/3)*2*pi*rUsing this arc ABC = 2/3 perimeter of triangle = 2(pi)r * 2/3
and we want 2r, so:
2r = 36/pi = approx. 11
I understood what Asamaverick wanted to say, but as testLuv noted, it s always good to use the exact terminology.
The answer is more than clear
Thanks.
Silvia
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selango
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I solved this with different approach.
Length of arc ABC=Length of arc AB+Length of arc BC
The inscribed angle in center is 120.
L arc AB=120/360*pi*d
L arc BC=120/360*pi*d
2/3*pi*d=24
d=11
Length of arc ABC=Length of arc AB+Length of arc BC
The inscribed angle in center is 120.
L arc AB=120/360*pi*d
L arc BC=120/360*pi*d
2/3*pi*d=24
d=11
