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?
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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.