Approaching Geometry Problems with Confidence and Strategic Thinking

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SUMMARY

The discussion focuses on solving a geometry problem involving chords AB and BC in a circle, with D as the midpoint of minor arc ADBC. The user seeks a strategic approach rather than a complete solution, specifically mentioning attempts with similar triangles and the sine law on triangles ADE and DBC. The conclusion emphasizes the importance of understanding geometric properties and relationships in circle geometry to tackle such problems effectively.

PREREQUISITES
  • Understanding of circle geometry and properties of chords
  • Knowledge of similar triangles and their applications
  • Familiarity with the sine law in triangle calculations
  • Ability to visualize geometric constructions and relationships
NEXT STEPS
  • Study the properties of chords in circles and their relationships
  • Learn about the midpoint theorem in circle geometry
  • Explore advanced applications of the sine law in various triangle configurations
  • Practice solving geometry problems involving arcs and angles
USEFUL FOR

Students and educators in geometry, particularly those looking to enhance their problem-solving skills and strategic thinking in circle-related problems.

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This is the last problem on a geometry problem set that I can't seem to finish.

AB and BC are chords in a circle where AB > BC. D is the midpoint of minor arc ADBC. If DE is perpendicular to AB, prove that AE = EB + BC.

I would really appreciate just the proper way to approach this question instead of a solution. I've tried joining CD and AC and using similar triangles but to no avail. I've also tried applying sine law on triangles ADE and DBC, no dice either.


Thanks in advance.
 
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I had to make an extension outside of the circle, but I got it!
 
well done son, solving your own question is like super medicine .
 

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