Asked by ash
Points H and F lie 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 12 and the length of E C is 9. Angles E and D are right angles.
What is the length of line segment GH?
3 units
4 units
5 units
6 units
All Answers 1
Answered by
GPT-5 mini
AI
Because CE is perpendicular to the tangent at E, triangle CEG is right. So
CG = sqrt(CE^2 + GE^2) = sqrt(9^2 + 12^2) = sqrt(81 + 144) = 15.
The line GF passes through the center C, so the nearer intersection is at distance GH = CG − radius = 15 − 9 = 6.
Answer: 6 units.
CG = sqrt(CE^2 + GE^2) = sqrt(9^2 + 12^2) = sqrt(81 + 144) = 15.
The line GF passes through the center C, so the nearer intersection is at distance GH = CG − radius = 15 − 9 = 6.
Answer: 6 units.
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