by nathi123 » Wed Dec 05, 2018 5:07 pm
[tex]OD=OC=R\Rightarrow \angle CDO=\angle OCD=x ; \triangle COD\Rightarrow \angle COD=180^\circ -2x ; CO=OB=R\Rightarrow \angle OCB=\angle OBC[/tex]
[tex]\angle OBC=90^\circ - x[/tex] [tex]( OB\bot AB ) \Rightarrow \angle OCB=\angle OBC =90^\circ - x\Rightarrow \angle COB=180^\circ -2(90^\circ -2x)=4x[/tex]
[tex]\Rightarrow \angle DOB=360^\circ - 4x-180^\circ +2x=180^\circ -2x ;[/tex]
for ABOD we have [tex]\angle ODA+\angle OBA+\angle DOB+y=360^\circ ; OD\bot AD\Rightarrow[/tex]
[tex]\angle ODA+ \angle OBA=180^\circ\Rightarrow 180^\circ -2x +y=180^\circ \Leftrightarrow y=2x[/tex]
[tex]OD=OC=R\Rightarrow \angle CDO=\angle OCD=x ; \triangle COD\Rightarrow \angle COD=180^\circ -2x ; CO=OB=R\Rightarrow \angle OCB=\angle OBC[/tex]
[tex]\angle OBC=90^\circ - x[/tex] [tex]( OB\bot AB ) \Rightarrow \angle OCB=\angle OBC =90^\circ - x\Rightarrow \angle COB=180^\circ -2(90^\circ -2x)=4x[/tex]
[tex]\Rightarrow \angle DOB=360^\circ - 4x-180^\circ +2x=180^\circ -2x ;[/tex]
for ABOD we have [tex]\angle ODA+\angle OBA+\angle DOB+y=360^\circ ; OD\bot AD\Rightarrow[/tex]
[tex]\angle ODA+ \angle OBA=180^\circ\Rightarrow 180^\circ -2x +y=180^\circ \Leftrightarrow y=2x[/tex]
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