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Problem 431: Quadrilateral, Midpoints of Diagonals, Transversal

The figure shows a quadrilateral ABCD. E and F are the midpoints of diagonals AC and BD. Line EF intersects AB and CD at G and H, respectively. Prove that AG.DH = BG.CH.

Quadrilateral, diagonal, midpoint, similarity

See also: Typography and poster of problem 431