Problem Solving

The points R, T, and 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] OA:D [/spoiler]

A circle by definition contains 360. The length of an arc relative to the circle circumference is directly proportionate to the arc degree.

Let x be arc degree so

length of the arc/circumference of circle=x/360


(4pi/3)/2pi*r=x/360

since r=4(given)

there fore

x=60 degrees

so given that radius is 4 then from figure OR=4 and OU=4

2 sides are equal it is an isoceles triange

so the other angle is 60.

since 2 angles are 60 the other angle is also 60 so it an equaliatera triangle so all sides are equal so

RU=4

I think my explanation is too long. I have made a word attachment which contains a rough figure
Suggest me if iam wrong.

Thanks,
Sibbineni

I too got the same answer. thanks for the answer. RT = 4 length units