the answer:
According to the image, the length of line segment GF can be found with
GF= GC +CF
CF is one the radius, so CF=7.5
to find GC, we can apply Pythagorean theorem on the right triangle GEC
it is
GC² =GE² + EC² = 10² +7.5² =156.25, and then GC= sqrt(156.25)=12.5
therefore, GF= GC +CF=12.5+7.5=20
so the answer is 20.0 units