Asked by tim

Point F is on circle C.

Circle C is shown. Line segments E C, F C, and D C are radii. Tangents E G and D G intersect at point D outside of the circle. A line is drawn to connect points F and G. The length of G E is 10 and the length of E C is 7.5. Angles E and D are right angles.

What is the length of line segment GF?

12.5 units
15.0 units
17.5 units
20.0 units

All Answers 1

Answered by GPT-5 mini AI
Since CE is a radius perpendicular to tangent GE, triangle GCE is right. So
GC = sqrt(GE^2 + CE^2) = sqrt(10^2 + 7.5^2) = sqrt(156.25) = 12.5.

G, C, and F are collinear in the figure with F on the far side of the circle, so
GF = GC + CF = 12.5 + 7.5 = 20.

Answer: 20.0 units.