Geometry Question

[sanaa.rizwan]

QR PS 153

The points R,T and U line on a circle that has a radius of 4. if the length of the arc RTU is 4П/3, what is the length of the line segment RU

a. 4/3
b. 8/3
c. 3
d. 4
e. 6

[Anju@Gurome]

The points R,T and U line on a circle that has a radius of 4. if the length of the arc RTU is 4П/3, what is the length of the line segment RU

Circumference of the circle = (2П)*(4) = 8П
Let x be the angle subtended at the center of circle.
Then, 8Пx/360 = 4П/3
x = 60, now RC and RU are equal so angles CRU and RUC should be equal. Hence, triangle RCU is an equilateral triangle with each angle 60º.

So, RU = 4

The correct answer is D.

[Deepthi Subbu]

Hi Anju@Gurome,
Since the qn says all the points lie on a circle, the measure of line segment RU is pretty much the same as finding x/360*2*pi*r. i understand that this repeats whats already given, but whats the difference here.?

Also can u illustrate with the help of a diagram pls?

[Anju@Gurome]

Hi Anju@Gurome,
Since the qn says all the points lie on a circle, the measure of line segment RU is pretty much the same as finding x/360*2*pi*r. i understand that this repeats whats already given, but whats the difference here.?

Also can u illustrate with the help of a diagram pls?

Refer to the diagram below,


What you've suggested gives us the length of the arc RTU.
But the problem asked for length of the line segment RU.

Hope that helps.