(CHALLENGING )Trigonometry / geometry proof

[Doctor_Doom]

(CHALLENGING!)Trigonometry / geometry proof

Hey guys I've spent a couple hours on this without even coming close. I'm hoping someone here can drop me a hint.

From the above image I need to proof that GL is R(THETA) in length. The only other information I have is that GT extended is a type of sheet (metal sheet) balancing and "rocking" forward and backward on the circular structure of radius R (cylinder).

Hints or help or links would be of HUGE assistance.

Thanks in advance!

 

[CompuChip]

Is there anything to prove?
If you have a circle of radius R, then a circular segment with angle theta has length R theta.
That's about the definition of radians (a unit circle goes around 2pi radians, and has circumference 2pi).

If you let G' be the marked point on the cylinder below G (near which the label for c is written), then G'T along the circle has length R theta. Since G is a point on the circle with center T which also goes through G' (as indicated by the circular arc), GT is also R theta.

 

[Doctor_Doom]

Thanks that makes sense. Anyone else have a proof for what was stated above?