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Arc of a circle

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Junior | Next Rank: 30 Posts
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by gmater29 » Fri Oct 23, 2009 4:55 am
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
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Senior | Next Rank: 100 Posts
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Re: Arc of a circle

by uttam.albela » Fri Oct 23, 2009 5:12 am
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
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Junior | Next Rank: 30 Posts
Posts: 23
Joined: Sat Oct 03, 2009 1:22 am
Location: Singapore

by gmater29 » Fri Oct 23, 2009 6:11 am
Thats the OA.. Thanks I'm doing some crazy silly mistakes..
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