Question

In a square ABCD, its diagonal AC and BD intersect each other at point O. The bisector of angle DAO meets BD at point M and bisector of angle ABD meets AC at N and AM at L. Show that - ALOB is a cyclic quadrilateral.

Answer 1

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

In quadrilateral ALOB,

∵ ∠ ABO + ∠ ALO = 45°  + 90° + 45°  = 180°

Therefore, ALOB is a cyclic quadrilateral.