How do you prove that AMON is cyclic?

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Answer 1 · 2017-11-11T05:51:25

given

Construction
#Aand O;Band O;Cand O;Mand O;Nand O;#are joined

In #DeltaONA and Delta ONC#

#OA=OC # radius of same circle

#ON# common side

#AN=CN# given

Hence #DeltaONA ~=Delta ONC#

So #/_ANO =/_CNO=90^@#

similarly #DeltaOMA ~=Delta OMB#

This means #/_AMO =/_BMO=90^@#

So #/_AMO+ANO=90^@# but these are opposite angles of the quadrilateral #AMON#.

Hence the quadrilateral #AMON# is cyclic.