Cap. 8 - Circunferencia I ⇒ Solucionário:Racso - Cap VIII - Problemas de Geometria y Como Resolverlos - I Edição - Ex:15 Tópico resolvido

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Problema Proposto
15 - Na figura se [tex3]\overset{\LARGE{\frown}}{APC}=240^o[/tex3] calcular x.

Resposta

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D) 30^o

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[tex3]\measuredangle GOH = 120^o\\
\\\measuredangle BGA=\measuredangle I+ \measuredangle A\\
\measuredangle EHC = \measuredangle D+ \measuredangle C \therefore \measuredangle BGA + \measuredangle EHC = \measuredangle I+ \measuredangle A+\measuredangle D+\measuredangle C \\
60^o =\measuredangle I+\measuredangle A+\measuredangle D+\measuredangle C ~mas~ I\measuredangle =\measuredangle A e \measuredangle D=\measuredangle C (\triangle_s~são ~isóscels)\\
60^o = 2\measuredangle I +2\measuredangle D \rightarrow \measuredangle I+\measuredangle D = 30^o \therefore \boxed{\color{red}x = 30^o(x ~é~externo ~ao~\triangle IND)}[/tex3]