h) AC = 9, BC = 5, ED = 12, CD =? i) ED = 8, DC = 4, FC =? i) FC = 6, ED = 9, CD =? F E
h) AC = 9, BC = 5, ED = 12, CD =? i) ED = 8, DC = 4, FC =? i) FC = 6, ED = 9, CD =? F 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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Question F & H please

Transcribed Image Text:Given that \( \overline{CF} \) is a tangent to the circle shown:

Transcribed Image Text:Below is a transcription of the mathematical problems, followed by a description of the geometric diagram:
### Transcription of the Problems
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) \( FC = 6, \, ED = 9, \, CD = ? \)
### Description of the Diagram
The diagram depicts a circle with several points and lines:
- The circle has points labeled \( A, B, C, D, E, \) and \( F \) on its circumference.
- Lines \( AC, BE, \) and \( CF \) are secant lines intersecting the circle.
- \( G \) is a point of intersection of segments \( BE \) and \( AC \) inside the circle.
- The line \( BE \) intersects the circle at points \( B \) and \( E \).
- Line \( AC \) passes through points \( A \) and \( C \).
- Line \( CF \) extends from point \( C \) and intersects the circle at point \( F \).
- Line \( DC \) is a segment inside the circle connecting points \( D \) and \( C \).
This setup suggests the use of properties of secant segments and lengths in a circle to solve the given problems.
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