The puzzle is quite simple if seen the right way.
Consider the triangle EFT. For the law of the sines:
ET/sin(EFT) = EF/sin(ETF)
ET=TS cos(ETS) =2EF cos(ETS)
From here: 2EF cos(ETS) sin(ETF)= EF sin(EFT)
but ETF=ETS
Then: 2 cos(ETS) sin(ETS) = sin(EFT); sin(2ETS) = sin(EFT)
ETS= EFT/2 (angles)
The puzzle asks for the ratio EFG/SFG
EFG=EFS + SFG = EFT + ETS = 3ETS =3SFG
Then EFG/SFG=3
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Edited on August 9, 2016, 10:40 am

Posted by armando
on 20160809 04:31:42 