Τρίτη, 10 Οκτωβρίου 2017

2007 JBMO Shortlist G4

Let $S$ be a point inside $\angle pOq$, and let $k$be a circle which contains $S$ and touches the legs $Op$ and $Oq$ in points $P$ and $Q$ respectively. Straight line $s$ parallel to $Op$ from $S$ intersects $Oq$ in a point $R$.   Let $T$  be the point of intersection of the ray $PS$ and circumscribed circle of $\vartriangle SQR$ and $T \ne  S$. Prove that $OT // SQ$ and $OT$ is a tangent of the circumscribed circle of $\vartriangle SQR$.

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