gmater29 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
Circumference of the circle = 2 * π * r = 8π
8Ï€ unit of length = 360 degree of angle at the centre
1 unit of length = 360 / 8Ï€ degree
4Ï€/3 unit of length = (360 * 4Ï€) / (8Ï€ * 3)= 60 degree
So the arc RTU is making angle of 60 degree at the centre.
Consider triange RUO. O is centre of the triangle.
Two side RO and UO are equal to 4 unit of length as they are equal to radius of the circle.
and angle ROU is 60 degree. So each angle will 60 Degree as sum of other 2 angle = 120 and as both sides are equal, so each angle 60 degrees.
Equilateral triangle.
Side RU = 4 unit
