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Proposed ProblemClick the figure below to see the complete problem 309.See also:Complete Problem 309Collection of Geometry ProblemsLevel: High School, SAT Prep, College geometry
Extend AC to J such that CJ = AB=BC=CD etc. Now angle(ACD)=140 -20=120 and thus angle(DCJ)=60. But, CJ==CD so triangle CJD is equilateral with angle(CJD)=60=angle(AED). This makes triangles AED & AJD congruent and therefore, AE=AJ=AC+AB. QED
Extend AB and ED to meet at X. Then Tr.s AEX and BDX are both equilateral and the result follows Sumith PeirisMoratuwaSri Lanka
I tried Ptolemy for cyclic quads but failed so far. Anyone can throw light on this?