a is 4/3 not 43

The answer is 4. Here's why:

We're given that arc RTU is 4pi/3 and that the radius is 4. From this information, we can assume that the diameter of the circle is 8 and use the formula for circumference to find out what degree measure makes arc RTU 4pi/3.

C=pi*diameter
C=8pi
x=degree measure
8pi*x/360=4pi/3
x=4pi/3*360/8pi=60 degrees

The length of RU intersects the two radii of the circle, which makes a triangle. Knowing that two sides of the triangle are going to be the same (because of the equal radii) and also knowing the angle RTU equals 60, we know that the triangle is equilateral. Since, RT=4 and TU=4, RU must also equal 4.

it's hard to visualize why RU is 4.

I get how it forms an isosceles triangle consisting of 2 radii with a 60 degree angle.. however i was lost after that..

Can someone help please?

Thanks in advance

Answer given to said problme is - A

but they didnt explain how they arrived at it

We know that the arc is 1/6 of the circumference (4pi/3 / 2pi4 (the length of circ.)= 1/6), so the angle ROU (O-center)=60 degrees.
We know that the two sides of the triangle ROU=4, so it is an isolesce triangle and since the measure of the angle ROU is 60 degrees, we can determine that this triangle is equilateral. So we can conclude that the line segment RU = 4.

We need to draw a diagram in order to better understand what the problem is asking.

See diagram attached