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e) CF %3D 6, АВ 3 5, ВС %3D? f) EG = 4, BC = 3, CD = ED, ED =? g) AC = 30, BC = 5, ED = 12, CD =? h) AC = 9, BC = 5, ED = 12, CD =? i) ED = 8, DC = 4, FC =? i) FC = 6, ED = 9, CD =?

e) CF %3D 6, АВ 3 5, ВС %3D? f) EG = 4, BC = 3, CD = ED, ED =? g) AC = 30, BC = 5, ED = 12, CD =? h) AC = 9, BC = 5, ED = 12, CD =? i) ED = 8, DC = 4, FC =? i) FC = 6, ED = 9, CD =?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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I need help with questions e-j please.

### Geometry Problem Set on Chords and Secants Below is a list of geometry problems based on a circle with various segments labeled: 1. **Find BC:** - \( CF = 6, AC = 12, BC = ? \) 2. **Find DG:** - \( AG = 3, BE = 10, BG = 4, DG = ? \) 3. **Find CE:** - \( AC = 12, BC = 4, DC = 3, CE = ? \) 4. **Find GE:** - \( AG = 8, GD = 5, BG = 10, GE = ? \) 5. **Find BC:** - \( CF = 6, AB = 5, BC = ? \) 6. **Find CD and ED:** - \( EG = 4, BC = 3, CD = ED, ED = ? \) 7. **Find CD:** - \( AC = 30, BC = 5, ED = 12, CD = ? \) 8. **Find CD:** - \( AC = 9, BC = 5, ED = 12, CD = ? \) 9. **Find FC:** - \( ED = 8, DC = 4, FC = ? \) 10. **Find CD:** - \( FC = 6, ED = 9, CD = ? \) ### Diagram Explanation The diagram illustrates a circle with several secants and chords intersecting at a point (G) outside the circle and a single point (D) on the circle: - The circle has points labeled A, B, C, D, E, F, and G. - Chord AB and chord CD intersect at point G inside the circle. - The line segments extend from point G to points A, C, E, and F. - Additional line extensions are labeled from the circle's circumference to external points, creating tangents and secants: AG, BE, and CF. - These geometric relationships suggest using properties of intersecting chords and tangent-secant theorems to solve the above problems.
Transcribed Image Text:### Geometry Problem Set on Chords and Secants Below is a list of geometry problems based on a circle with various segments labeled: 1. **Find BC:** - \( CF = 6, AC = 12, BC = ? \) 2. **Find DG:** - \( AG = 3, BE = 10, BG = 4, DG = ? \) 3. **Find CE:** - \( AC = 12, BC = 4, DC = 3, CE = ? \) 4. **Find GE:** - \( AG = 8, GD = 5, BG = 10, GE = ? \) 5. **Find BC:** - \( CF = 6, AB = 5, BC = ? \) 6. **Find CD and ED:** - \( EG = 4, BC = 3, CD = ED, ED = ? \) 7. **Find CD:** - \( AC = 30, BC = 5, ED = 12, CD = ? \) 8. **Find CD:** - \( AC = 9, BC = 5, ED = 12, CD = ? \) 9. **Find FC:** - \( ED = 8, DC = 4, FC = ? \) 10. **Find CD:** - \( FC = 6, ED = 9, CD = ? \) ### Diagram Explanation The diagram illustrates a circle with several secants and chords intersecting at a point (G) outside the circle and a single point (D) on the circle: - The circle has points labeled A, B, C, D, E, F, and G. - Chord AB and chord CD intersect at point G inside the circle. - The line segments extend from point G to points A, C, E, and F. - Additional line extensions are labeled from the circle's circumference to external points, creating tangents and secants: AG, BE, and CF. - These geometric relationships suggest using properties of intersecting chords and tangent-secant theorems to solve the above problems.
### Geometry Problem Set: Tangent and Circle Relations Given that \( \overline{CF} \) is a tangent to the circle shown, solve for the unknown variables in each scenario: a) \( CF = 6, AC = 12, BC = ? \) b) \( AG = 3, BE = 10, BG = 4, DG = ? \) c) \( AC = 12, BC = 4, DC = 3, CE = ? \) d) \( AG = 8, GD = 5, BG = 10, GE = ? \) e) \( CF = 6, AB = 5, BC = ? \) f) \( EG = 4, BC = 3, CD = ED, ED = ? \) g) \( AC = 30, BC = 5, ED = 12, CD = ? \) h) \( AC = 9, BC = 5, ED = 12, CD = ? \) i) \( ED = 8, DC = 4, FC = ? \) j) \( FC = 6, ED = 9, CD = ? \) ### Explanation of Concepts: - **Tangent to a Circle**: A line that touches the circle at exactly one point. - **Segment Relationships**: Use properties of tangents, chords, secants, and inscribed angles to solve for unknown variables. Typically involves the Pythagorean theorem, and the Power of a Point theorem. By applying these principles, solve for the unknown segments in the problems provided.
Transcribed Image Text:### Geometry Problem Set: Tangent and Circle Relations Given that \( \overline{CF} \) is a tangent to the circle shown, solve for the unknown variables in each scenario: a) \( CF = 6, AC = 12, BC = ? \) b) \( AG = 3, BE = 10, BG = 4, DG = ? \) c) \( AC = 12, BC = 4, DC = 3, CE = ? \) d) \( AG = 8, GD = 5, BG = 10, GE = ? \) e) \( CF = 6, AB = 5, BC = ? \) f) \( EG = 4, BC = 3, CD = ED, ED = ? \) g) \( AC = 30, BC = 5, ED = 12, CD = ? \) h) \( AC = 9, BC = 5, ED = 12, CD = ? \) i) \( ED = 8, DC = 4, FC = ? \) j) \( FC = 6, ED = 9, CD = ? \) ### Explanation of Concepts: - **Tangent to a Circle**: A line that touches the circle at exactly one point. - **Segment Relationships**: Use properties of tangents, chords, secants, and inscribed angles to solve for unknown variables. Typically involves the Pythagorean theorem, and the Power of a Point theorem. By applying these principles, solve for the unknown segments in the problems provided.
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