Q. The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*(pi)/3, what is the length of line segment RU?
A. 4/3 B. 8/3 C. 3 D. 4 E. 6
A. 4/3 B. 8/3 C. 3 D. 4 E. 6
Circumference of the circle = 2(pi)(4) = 8(pi)amp0201 wrote:Q. The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*(pi)/3, what is the length of line segment RU?
A. 4/3 B. 8/3 C. 3 D. 4 E. 6
Let x be the angle subtended at the center of circle.
Then (x)(8)(pi)/360 = 4(pi)/3
x = 60, now RC and RU are equal so angles CRU and RUC should be equal. Hence, triangle RCU is an equilateral triangle with each angle 60º.
So, RU = 4
The correct answer is D.
