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Question-173273




Question Number 173273 by mr W last updated on 09/Jul/22
Commented by mr W last updated on 09/Jul/22
find the maximum area of green  inscribed circle=?
$${find}\:{the}\:{maximum}\:{area}\:{of}\:{green} \\ $$$${inscribed}\:{circle}=? \\ $$
Answered by mr W last updated on 09/Jul/22
Commented by mr W last updated on 09/Jul/22
AM=(√(10^2 +5^2 ))=5(√5)  r=radius of green circle  SM=5−2r  AN=10−2r  AM=10−2r+2r+5−2r  5(√5)=15−2r  ⇒r=((5(3−(√5)))/2)  A_(green) =πr^2 =((25(7−3(√5))π)/2)
$${AM}=\sqrt{\mathrm{10}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} }=\mathrm{5}\sqrt{\mathrm{5}} \\ $$$${r}={radius}\:{of}\:{green}\:{circle} \\ $$$${SM}=\mathrm{5}−\mathrm{2}{r} \\ $$$${AN}=\mathrm{10}−\mathrm{2}{r} \\ $$$${AM}=\mathrm{10}−\mathrm{2}{r}+\mathrm{2}{r}+\mathrm{5}−\mathrm{2}{r} \\ $$$$\mathrm{5}\sqrt{\mathrm{5}}=\mathrm{15}−\mathrm{2}{r} \\ $$$$\Rightarrow{r}=\frac{\mathrm{5}\left(\mathrm{3}−\sqrt{\mathrm{5}}\right)}{\mathrm{2}} \\ $$$${A}_{{green}} =\pi{r}^{\mathrm{2}} =\frac{\mathrm{25}\left(\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}\right)\pi}{\mathrm{2}} \\ $$
Commented by Tawa11 last updated on 11/Jul/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$

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