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Question-149720




Question Number 149720 by cherokeesay last updated on 06/Aug/21
Answered by mr W last updated on 06/Aug/21
(R−1)^2 +(R−2)^2 =R^2   R^2 −6R+5=0  (R−5)(R−1)=0  ⇒R=5, 1 (rejected)  area of semicircle=((πR^2 )/2)=((25π)/2)
$$\left({R}−\mathrm{1}\right)^{\mathrm{2}} +\left({R}−\mathrm{2}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$${R}^{\mathrm{2}} −\mathrm{6}{R}+\mathrm{5}=\mathrm{0} \\ $$$$\left({R}−\mathrm{5}\right)\left({R}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{R}=\mathrm{5},\:\mathrm{1}\:\left({rejected}\right) \\ $$$${area}\:{of}\:{semicircle}=\frac{\pi{R}^{\mathrm{2}} }{\mathrm{2}}=\frac{\mathrm{25}\pi}{\mathrm{2}} \\ $$

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