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27 Oct 2010, 09:14
Kudos
Bookmarks
I found this question on a sample GMAT test online. It's driving me crazy as I cannot find out how to get the answer.
Here you go;
The points R, T, U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?
A. 4/3
B. 8/3
C. 3
D. 4
E. 6
Spoiler (answer is 4) how do we get that solution???
Here you go;
The points R, T, U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?
A. 4/3
B. 8/3
C. 3
D. 4
E. 6
Spoiler (answer is 4) how do we get that solution???
27 Oct 2010, 09:43
Kudos
Bookmarks
Let's assume the center of the circle is O. Angle formed by the arc RTU is angle(ROU)
Length of the arc "RTU" can be deduced by the formula
(angle(ROU) / 360)*2*pi*r
where r is the radius of the circle.
Equating the above formula to 4pi/3, we can get the angle formed by the arc. And turns out that this angle is 60deg. Now consider triangle RUO. It's an equilateral triangle (given that two sides are equal and the angle between them is 60deg, which means the remaining angles of the triangle are also 60deg).
Hence the length of RU is 4. (choice D).
Length of the arc "RTU" can be deduced by the formula
(angle(ROU) / 360)*2*pi*r
where r is the radius of the circle.
Equating the above formula to 4pi/3, we can get the angle formed by the arc. And turns out that this angle is 60deg. Now consider triangle RUO. It's an equilateral triangle (given that two sides are equal and the angle between them is 60deg, which means the remaining angles of the triangle are also 60deg).
Hence the length of RU is 4. (choice D).
