Data Sufficiency (DS) | In the diagram below, PQ is a diameter of the circle having center at

We have \(\widehat{POS}=180^o -2\widehat{SPO}\)

Also \(\widehat{POS}=\widehat{POR}+\widehat{ROS}\)

We also have \(\widehat{POR} = 180^o -2\widehat{RPO}\)

Hence \(\widehat{POS}=\widehat{POR}+\widehat{ROS} \\
\implies 180^o -2\widehat{SPO} = 180^o -2\widehat{RPO} +\widehat{ROS} \\
\implies \widehat{ROS} = 2\widehat{RPO}
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