In a square ABCD,its diagonal AC and BD intersect eachother at point O The bisector of angle DAO meets BD - Maths -

Question

In a square ABCD,its diagonal AC and BD intersect eachother 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:
(a)angle ONL+angle OML=180 degree
(b)angle BAM=angle BMA
(c)ALOB is a cyclic quadrilateral

Sunanta Meitei · Accepted Answer

Hi! Here is the answer to your question ABCD is a square

(c) In quadrilateral OMNL, ∠ONL + ∠OML + ∠NOM + ∠NLM = 360° ⇒ 180° + 90° + ∠NLM = 360° [∠ONL + ∠OML = 180°] ⇒ ∠NLM = 90° ∠NLM + ∠ALB = 180° ⇒ 90° + ∠ALB = 180° ⇒ ∠ALB = 90° ∠ALB = ∠AOB (Each 90°) It is known that If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i e they are concyclic) Thus, ALOB is a cyclic quadrilateral Cheers!

In a square ABCD,its diagonal AC and BD intersect eachother 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: (a)angle ONL+angle OML=180 degree. (b)angle BAM=angle BMA (c)ALOB is a cyclic quadrilateral.

In a square ABCD,its diagonal AC and BD intersect eachother 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:

(a)angle ONL+angle OML=180 degree.

(b)angle BAM=angle BMA

(c)ALOB is a cyclic quadrilateral.