Question Number 210688 by BHOOPENDRA last updated on 16/Aug/24
$$ \\ $$In a convex quadrilateral ABCD, diagonals AC and BD intersect at E, while perpendicular bisectors of AB and CD intersect at F, and those of BC and DA intersect at G. Prove: (1) E, F, and G are collinear, (2) AE:EC = BF:FD, and (3) CG:GD = AF:FB.
Commented by A5T last updated on 17/Aug/24
$${E},{F}\:{and}\:{G}\:{are}\:{not}\:{always}\:{collinear}.\:{You}\:{can} \\ $$$${check}\:{by}\:{constructing}\:{some}\:{quadrilaterals}\:{with} \\ $$$${satisfied}\:{conditions}. \\ $$