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?

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 2016-08-16 10:26:23