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Angle Ratio Ascertainment 6 (Posted on 20160814) 

The point T is located in the interior of triangle EFG such that: :
∠TEF = ∠TEG=(∠FEG + ∠EGF)/4
S denotes the foot of the angle bisector of ∠EFG
The line TS is extended to meet the circumcircle of triangle ETG at point U
Find ∠EUF/∠FUG
What am I missing? (spoiler)

 Comment 1 of 2

What
am I missing?
The condition that /TEF = /TEG
= (/FEG + /EGF)/4 would seem to
imply that /FEG = /FGE, making triangle EFG isosceles, so that
FS is the perpendicular bisector of EG and passes through the
centre of the circumcircle of triangle ETG.
The ratio /EUF//FUG seems to change as T moves whereas the
problem seems to imply that it might be constant.
Help needed – perhaps from someone with a geometry package…

Posted by Harry
on 20160816 10:26:23 


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