Geometry question

[MonicaKhan]

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.

[jayhawk2001]

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 question and answer are both correct.

The length of arc ABC = 2/3 * perimeter of the circle.

2/3 * 2*pi*r = 24
2*r = 11

Hence C

[Tame the CAT]

Hey Jay, how do you know the length of ABC is 2/3 the perimeter of the circle

[jayhawk2001]

Hey Jay, how do you know the length of ABC is 2/3 the perimeter of the circle

Since it is an equilateral triangle, arc AB = arc BC = arc CA.
Also, arc AB + BC + CA = perimeter of the circle.

Hence ARC ABC = 2/3 * perimeter of the circle

[rajeshvellanki]

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

[Tame the CAT]

Absolutely right. Thanks!