Mathematics

In a square ABCD, its diagonals AC and BD intersect each other at point O. The bisector of angle DAO meets BD at point M and the bisector of angle ABD meets AC at N and AM at L. Show that :

(i) ∠ONL + ∠OML = 180°

(ii) ∠BAM = ∠BMA

(iii) ALOB is a cyclic quadrilateral.

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