Circumference of the circle = 2(pi)(4) = 8(pi)alex.gellatly wrote:The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is {4pi}/3, what is the length f line segment RU?
A. 4/3
B. 8/3
C. 3
D. 4
E. 6
Thanks
Why must the other 2 sides be equal?Jim@StratusPrep wrote:The length of the circumference is Pi times diameter or 8pi in this case
8pi/6 = 4pi/3, so the arc is 1/6th of the circumference, which means the central angle is 1/6 or 360 or 60 degrees. Since the other 2 sides must be equal, this is an equilateral triangle. As the other sides are radii, their length is 4, which is the same as RU
Answer D.
I am guessing you are ok till the part of upto the central angle being 60 degrees.alex.gellatly wrote:Why must the other 2 sides be equal?Jim@StratusPrep wrote:The length of the circumference is Pi times diameter or 8pi in this case
8pi/6 = 4pi/3, so the arc is 1/6th of the circumference, which means the central angle is 1/6 or 360 or 60 degrees. Since the other 2 sides must be equal, this is an equilateral triangle. As the other sides are radii, their length is 4, which is the same as RU
Answer D.
I'm sorry... but I still don't understand this question. Could someone explain differently?
Thanks
Sorry.. but I still don't get it. I understand how and why the central angle must be 60. However, I don't understand why the lengths are equal to R. Maybe if I had a visual representation or something. I've tried to draw it out... but I'm not following.eagleeye wrote:I am guessing you are ok till the part of upto the central angle being 60 degrees.alex.gellatly wrote:Why must the other 2 sides be equal?Jim@StratusPrep wrote:The length of the circumference is Pi times diameter or 8pi in this case
8pi/6 = 4pi/3, so the arc is 1/6th of the circumference, which means the central angle is 1/6 or 360 or 60 degrees. Since the other 2 sides must be equal, this is an equilateral triangle. As the other sides are radii, their length is 4, which is the same as RU
Answer D.
I'm sorry... but I still don't understand this question. Could someone explain differently?
Thanks
Now the other two sides are both radii of the circle. Hence they are both equal to 4. So we have one angle = 60, the other two sides (which are two radii) = 4.
If two sides are equal and one angle is 60, the other two angles must be 60 as well. (2x+60 = 180 => 2x=120 => x=60). Since all three angles are 60, it is an equilateral triangle. So all three sides are equal. Since the other 2 sides are the radii each of length 4, the third one is 4 also.
Did this help ?
alex.gellatly wrote:Sorry.. but I still don't get it. I understand how and why the central angle must be 60. However, I don't understand why the lengths are equal to R. Maybe if I had a visual representation or something. I've tried to draw it out... but I'm not following.eagleeye wrote:I am guessing you are ok till the part of upto the central angle being 60 degrees.alex.gellatly wrote:Why must the other 2 sides be equal?Jim@StratusPrep wrote:The length of the circumference is Pi times diameter or 8pi in this case
8pi/6 = 4pi/3, so the arc is 1/6th of the circumference, which means the central angle is 1/6 or 360 or 60 degrees. Since the other 2 sides must be equal, this is an equilateral triangle. As the other sides are radii, their length is 4, which is the same as RU
Answer D.
I'm sorry... but I still don't understand this question. Could someone explain differently?
Thanks
Now the other two sides are both radii of the circle. Hence they are both equal to 4. So we have one angle = 60, the other two sides (which are two radii) = 4.
If two sides are equal and one angle is 60, the other two angles must be 60 as well. (2x+60 = 180 => 2x=120 => x=60). Since all three angles are 60, it is an equilateral triangle. So all three sides are equal. Since the other 2 sides are the radii each of length 4, the third one is 4 also.
Did this help ?
