Question

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

Answer 1

ABCD is a square whose diagonals AC and BD intersect each other at right angles at O.

Therefore, ALOB is a cyclic quadrilateral.