Approaching Geometry Problems with Confidence and Strategic Thinking

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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!

 

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well done son, solving your own question is like super medicine .