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Question Number 198907 by a.lgnaoui last updated on 25/Oct/23
find the Area betwen Circle 1 and   Circle2.
$$\mathrm{find}\:\mathrm{the}\:\mathrm{Area}\:\mathrm{betwen}\:\mathrm{Circle}\:\mathrm{1}\:\mathrm{and}\: \\ $$$$\mathrm{Circle2}. \\ $$
Commented by a.lgnaoui last updated on 25/Oct/23
Commented by Rasheed.Sindhi last updated on 26/Oct/23
CD touches circle2 at point O (say)  AC^2 −AO^2 =OC^2    R^2 −r^2 =(7/2)^2      πR^2 −πr^2 =((49)/4)π    circle1^(area) −circle2^(area) =((49)/4)π
$$\mathrm{CD}\:{touches}\:{circle}\mathrm{2}\:{at}\:{point}\:\mathrm{O}\:\left({say}\right) \\ $$$$\mathrm{AC}^{\mathrm{2}} −\mathrm{AO}^{\mathrm{2}} =\mathrm{OC}^{\mathrm{2}} \\ $$$$\:\mathrm{R}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} =\left(\mathrm{7}/\mathrm{2}\right)^{\mathrm{2}} \:\: \\ $$$$\:\pi\mathrm{R}^{\mathrm{2}} −\pi\mathrm{r}^{\mathrm{2}} =\frac{\mathrm{49}}{\mathrm{4}}\pi \\ $$$$\:\:\overset{\mathrm{area}} {\mathrm{circle1}}−\overset{\mathrm{area}} {\mathrm{circle2}}=\frac{\mathrm{49}}{\mathrm{4}}\pi\:\: \\ $$

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