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.
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.
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