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Let $\mathcal{R}$ be the circle centered at $(0,0)$ with radius $15.$  The lines $x = 8$ and $y = 1$ divide $\mathcal{R}$ into four regions $\mathcal{R}_1$, $\mathcal{R}_2$, $\mathcal{R}_3$, and $\mathcal{R}_4$.  Let $[\mathcal{R}_i]$ denote the area of region $\mathcal{R}_i$.  If
\[[\mathcal{R}_1] > [\mathcal{R}_2] > [\mathcal{R}_3] > [\mathcal{R}_4],\]
then find $[\mathcal{R}_1] + [\mathcal{R}_2] + [\mathcal{R}_3] + [\mathcal{R}_4]$.

 Nov 8, 2023

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