Solve this Geometry Problem using Alternate Segments

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SUMMARY

The discussion focuses on solving a geometry problem involving the tangent-chord theorem, specifically addressing the incorrect value of angle AEG, which is stated as 160 degrees. Participants emphasize that the solution misapplies the tangent-chord theorem by incorrectly using a quadrilateral instead of a triangle. The correct relationships are established as angle EAB equals angle BEF and angle AEG equals angle ABE, highlighting the necessity of proper theorem application in geometric proofs.

PREREQUISITES
  • Understanding of the tangent-chord theorem
  • Knowledge of angle relationships in triangles
  • Familiarity with geometric proofs
  • Ability to analyze geometric figures
NEXT STEPS
  • Study the properties of the tangent-chord theorem in detail
  • Explore angle relationships in triangles and quadrilaterals
  • Practice solving geometry problems involving the tangent-chord theorem
  • Review common mistakes in geometric proofs and how to avoid them
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Students studying geometry, educators teaching geometric concepts, and anyone interested in improving their problem-solving skills in mathematics.

chwala
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Homework Statement
see attached.
Relevant Equations
Tangent- chord theorem
This is a textbook problem...clearly angle ##AEG≠ 160^0## there is something wrong with the value given,...I am trying to analyse this...

1636416319751.png
 
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The solution misuses tangent chord theorem.
Exact ones are
angle EAB= angle BEF
angle AEG= angle ABE
 
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anuttarasammyak said:
The solution misuses tangent chord theorem.
Exact ones are
angle EAB= angle BEF
angle AEG= angle ABE
That is correct, ...and exactly my thoughts. We ought to make use of the triangle only in establishing the tangent- chord theorem and not the quadrilateral...
 

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