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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
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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