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Question Number 175894 by cortano1 last updated on 09/Sep/22

Answered by mr W last updated on 09/Sep/22

Commented by mr W last updated on 09/Sep/22

a^2 =10^2 +(a−5)^2   ⇒a=12.5  (a+R)^2 =a^2 +(10−R)^2   (20+2a)R=100  ⇒R=((100)/(45))=((20)/9) ✓

$${a}^{\mathrm{2}} =\mathrm{10}^{\mathrm{2}} +\left({a}−\mathrm{5}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{a}=\mathrm{12}.\mathrm{5} \\ $$$$\left({a}+{R}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} +\left(\mathrm{10}−{R}\right)^{\mathrm{2}} \\ $$$$\left(\mathrm{20}+\mathrm{2}{a}\right){R}=\mathrm{100} \\ $$$$\Rightarrow{R}=\frac{\mathrm{100}}{\mathrm{45}}=\frac{\mathrm{20}}{\mathrm{9}}\:\checkmark \\ $$

Commented by cortano1 last updated on 10/Sep/22

nice

$$\mathrm{nice} \\ $$

Commented by Tawa11 last updated on 15/Sep/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

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