Consider triangle EFG with ∠EGF=90^o
ET is drawn parallel to FG, such that
T and F are located on opposite sides of EG, and
FT intersects EG at S, and
ST = 2EF

Find ∠EFG/∠SFG

Let U, V be the mid-points of TS, ES, respectively.

EF = US = UE    (since triangles EUV, SUV congruent),

therefore /EFS   = /EUS              (triangle EUF isosceles),
                        = 2 /SUV           (triangles EUV, SUV congruent),
                        = 2 /SFG           (triangles SUV, SFG similar).

Thus   /EFG = /EFS + /SFG = 3 /SFG

giving:  /EFG / /SFG  =  3

Posted by Harry on 2016-08-09 14:24:54