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Category: Coordinate Geometry

Question-59000

Question Number 59000 by Learner last updated on 03/May/19 Answered by MJS last updated on 03/May/19 $$\mathrm{the}\:\mathrm{centers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{small}\:\mathrm{circles}\:\mathrm{form}\:\mathrm{a}\:\mathrm{square} \\ $$$$\mathrm{with}\:\mathrm{side}\:\mathrm{length}\:\mathrm{2}{r}\:\Rightarrow\:\mathrm{its}\:\mathrm{diagonal}\:=\mathrm{2}\sqrt{\mathrm{2}}{r}\:\Rightarrow \\ $$$$\Rightarrow\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{big}\:\mathrm{circle}\:=\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){r}\:\Rightarrow \\ $$$$\Rightarrow\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area}\:=\left[\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){r}\right]^{\mathrm{2}} \pi−\mathrm{4}{r}^{\mathrm{2}} \pi=…