Please edit your post above so that the correct answer is hidden by the spoiler function, as I have done here:
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. 34
B. 38
C. 3
D. 4
E. 6
OA: D
C = 2Ï€r = 2*Ï€*4 = 8Ï€.
(arc RTU)/(circumference) = (4Ï€/3) / (8Ï€) = 1/6.
Since arc RTU is 1/6 of the circumference, ∠ROU -- the central angle that intercepts arc RTU -- constitutes 1/6 of 360º:
∠ROU = 1/6 * 360 = 60.
In ∆ROU, RO and UO are both radii, so RO = UO.
Since RO = UO, ∠ORU = ∠RUO, implying that ∠ORU = ∠RUO= 60.
Thus, ∆ROU is an equilateral triangle with a side of 4, implying that RU = 4.
The correct answer is
D.
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