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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.
Solution
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.
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