All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Angle Ratio Ascertainment 6 (Posted on 2016-08-14)
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

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 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 2016-08-16 10:26:23

 Search: Search body:
Forums (1)