How do you prove that AMON is cyclic?

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1 Answer
Nov 11, 2017

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.