# a problem of Geometry

in Tetrahedral ABCD : E,F and G are to order Middle of sides AB , BC, AD . also GE is Perpendicular to AB and GF is Perpendicular to BC . if angle of ABC is 96 degree . calculate angle of ACD?

-
The angle $\angle ACD$ seems to be independent of the angle $\angle ABC$. Is this what you meant to ask about? See my answer. – user12477 Nov 29 '12 at 10:24
a problem exist and that is this lines from G point may not perpendicular bisector , it means we only know this lines is perpendicular(may not bisector). – agustin Nov 29 '12 at 20:11
ok,that's right. since|AE|=|EB|then [GE] (perpendicular to [AB]) turn out to perpendicular bisector to [AB].also in same way [GF] turn out to perpendicular bisector to [BC]. – agustin Nov 30 '12 at 8:31

The line EG is the perpendicular bisector of the segment [AB] and so |AG|=|BG|. Likewise, the line FG is the perpendicular bisector of the segment [BC] and so |BG|=|CG|. G is the midpoint of the segment [AD] and so |AG|=|DG|. Thus the points A,B,C,D all lie on a circle with centre G. The angle $\angle ACD$ stands on the diameter $[AD]$, and so is a right angle.