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Let $$\mathcal{R}$$ be the circle centered at $$(0,0)$$ with radius $$10.$$ The lines $$x=6$$ and $$y=5$$ divide $$\mathcal{R}$$ into four regions $$\mathcal{R}_1, \mathcal{R}_2,\mathcal{R}_3,\mathcal{R}_4$$ . 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 $$[\mathcal{R}_1] - [\mathcal{R}_2] - [\mathcal{R}_3] + [\mathcal{R}_4]$$.

(I got 84 but that answer is wrong.) :(

Thank you so much for all your help!

May 31, 2020

#1
+30903
+1

As follows:

Needs to be carefully checked!

Jun 1, 2020