the answer:
the full question is as follow:
Point F is on circle C. What is the length of line segment GF?
12.5 units
15.0 units
17.5 units
20.0 units
according to the image, GF= GC + CF
CF is the radius of the circle, so it is CF =CE = 7.5
all that we want to find is the value of GC
let's consider the triangle GEC. This is a right triangle, so for finding GC, we can apply Pythagorean theorem
that is, GE² + EC² = GC², and from this, we have GC = sqrt(GE² + EC² )
GC = sqrt(10² + 7.5² )=sqrt(56.25)=12.5
therefore, GF= GC + CF=12.5 + 7.5 = 20.0
the answer is 20.0 units
