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Question Number 28690 by ajfour last updated on 28/Jan/18

Commented by ajfour last updated on 28/Jan/18

$$Findtheareainblueintermsof$$$$\mathit{r}and\mathit{d}.$$

Commented by beh.i83417@gmail.com last updated on 29/Jan/18

Commented by beh.i83417@gmail.com last updated on 29/Jan/18

$${om}^2={on}^2-r^2={(d+r)}^2-r^2=d(d+2r)$$$$om=\sqrt{d(d+2r)}$$$$cos\phi =\frac{r}{d+r}\Rightarrow \phi ={cos}^{-1}\frac{r}{d+r}$$$$S_{o\stackrel{△}{mn}}=\frac{1}{2}.om.r=\frac{1}{2}.r\sqrt{d(d+2r)}$$$$S_{sector}=\frac{1}{2}.r^2.\phi =\frac{1}{2}{r}^2.{cos}^{-1}\frac{r}{d+r}.$$$$S_{blue}=\frac{1}{2}r.\sqrt{d(d+2r)}-\frac{1}{2}{r}^2.{cos}^{-1}\frac{r}{d+r}.$$

Commented by beh.i83417@gmail.com last updated on 29/Jan/18

$$thankyoumaster.corrected.$$

Commented by ajfour last updated on 29/Jan/18

$$ThanksforsolvingSir.$$

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