hazelnut01 wrote:The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Ï€/3, what is the length of line segment RU?
A. 4/3
B. 8/3
C. 3
D. 4
E. 6
We can let the center of the circle be C. Since the radius of circle C is 4, its circumference is 2Ï€r = 2Ï€(4) = 8Ï€.
We can use the following proportion to determine the central angle that intercepts arc RTU:
x/360 = (4Ï€/3)/8Ï€
x/360 = 4Ï€/24Ï€
x/360 = 1/6
x = 60
Now triangle RUC (i.e., the triangle formed by radii RC and UC and chord RU) is at least an isosceles triangle, since RC = UC = 4. However, since x = 60 degrees, or angle RCU = 60 degrees, triangle RUC must be equilateral because angles RUC and URC are also 60 degrees. Since triangle RUC is equilateral, RU = RC = 4.
Answer:
D
