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 =? %3D i) ED = 8, DC = 4, FC =? %3D i) FC = 6, ED = 9, CD =? D A G E

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Chapter2: Second-order Linear Odes
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### Geometry Problems: Circle and Secants

This section consists of problems related to circle geometry, specifically involving segments and secants intersecting a circle.

**Problems:**

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) \( FC = 6, ED = 9, CD = ? \)

**Diagram Explanation:**

The diagram shows a circle with several points marked on and around it, connected by lines:
- Points \( A, B, C, D, E, F, \) and \( G \) are denoted around and inside the circle.
- \( AB \) and \( CD \) are secants intersecting inside the circle at point \( G \).
- \( EF \) is another secant, and point \( D \) is on this line.
- Segment \( AG \) is part of secant \( AB \).
- Segment \( BG \) is the remaining part of secant \( AB \) after point \( G \).
- Segment \( DC \) is part of secant \( CD \).

The problems above involve calculating unknown segment lengths using properties of secants and circles, likely employing the Power of a Point theorem or similar geometric principles.
Transcribed Image Text:### Geometry Problems: Circle and Secants This section consists of problems related to circle geometry, specifically involving segments and secants intersecting a circle. **Problems:** 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) \( FC = 6, ED = 9, CD = ? \) **Diagram Explanation:** The diagram shows a circle with several points marked on and around it, connected by lines: - Points \( A, B, C, D, E, F, \) and \( G \) are denoted around and inside the circle. - \( AB \) and \( CD \) are secants intersecting inside the circle at point \( G \). - \( EF \) is another secant, and point \( D \) is on this line. - Segment \( AG \) is part of secant \( AB \). - Segment \( BG \) is the remaining part of secant \( AB \) after point \( G \). - Segment \( DC \) is part of secant \( CD \). The problems above involve calculating unknown segment lengths using properties of secants and circles, likely employing the Power of a Point theorem or similar geometric principles.
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