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-collin

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

$${E},{F}\:{and}\:{G}\:{are}\:{not}\:{always}\:{collinear}.\:{You}\:{can} \\ $$$${check}\:{by}\:{constructing}\:{some}\:{quadrilaterals}\:{with} \\ $$$${satisfied}\:{conditions}. \\ $$

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