An equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approx. diameter of the circle?
A) 5
B) 8
C) 11 (this is the answer)
D) 15
E) 19
I suspect that the question stem might may have a flaw - it should read "radius," instead of "diameter."
Any help would be greatly appreciated.
Geometry question
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The question and answer are both correct.MonicaKhan wrote:An equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approx. diameter of the circle?
A) 5
B) 8
C) 11 (this is the answer)
D) 15
E) 19
I suspect that the question stem might may have a flaw - it should read "radius," instead of "diameter."
Any help would be greatly appreciated.
The length of arc ABC = 2/3 * perimeter of the circle.
2/3 * 2*pi*r = 24
2*r = 11
Hence C
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Since it is an equilateral triangle, arc AB = arc BC = arc CA.Tame the CAT wrote:Hey Jay, how do you know the length of ABC is 2/3 the perimeter of the circle
Also, arc AB + BC + CA = perimeter of the circle.
Hence ARC ABC = 2/3 * perimeter of the circle
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same explanation but in my way.
since it is an equilateral triangle all arc's are egual in lengh(draw it for more clear picture) since he gave sum of 2 sides=24 ==> each side=12
Perimeter=(3*12)=2*pi*r
2*r=36/pi
==> 2*r=11.34=11(approx)
R
since it is an equilateral triangle all arc's are egual in lengh(draw it for more clear picture) since he gave sum of 2 sides=24 ==> each side=12
Perimeter=(3*12)=2*pi*r
2*r=36/pi
==> 2*r=11.34=11(approx)
R
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