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## The Inscribed Angle Theorem without the Triangle Angle Sum Theorem

via hyperpallium in this question on the Mathematics Stack Exchange Of course, $$\overline{OP}\cong\overline{OR}\;\Leftrightarrow\;\angle RPO = \angle PRO$$. And then $$\angle RPQ = \angle PRS \quad\Leftrightarrow\quad \overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\quad\Leftrightarrow\quad\angle ROQ = \angle ORS = 2\angle RPQ$$ This base case of the Inscribed Angle Theorem is typically proven by way of the Triangle Angle Sum Theorem (perhaps in […]

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