Approaching Geometry Problems with Confidence and Strategic Thinking

AI Thread Summary
To approach the geometry problem involving chords AB and BC in a circle, focus on the properties of the circle and the relationships between the segments. Consider using the midpoint D of the minor arc ADBC to establish key angles and segments. Analyzing the triangle relationships and applying the Pythagorean theorem may also provide insights. The use of perpendicular lines, like DE to AB, can help in visualizing the problem. Ultimately, breaking down the problem into smaller, manageable parts can lead to a clearer understanding and solution.
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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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