Advanced Geometric Problem & Solution (Twice a week update) Now 4511 problems posted.
<Polygon-2023-258>, hint
Let <XBA=<XEA=Q then <XAE=36-Q. By trigonometry
AX+EX+CX=BX+DX is equivalent to ⇔ sinQ+sin(36-Q)+sin(72+Q)=sin(36+Q)+sin(72-Q)⇒
sinQ=2sinQ(cos36-cos72) , done.
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