Question Number 206572 by mr W last updated on 18/Apr/24
Commented by mr W last updated on 18/Apr/24
$${radius}\:{of}\:{circles}\:{is}\:\mathrm{1}. \\ $$$${find}\:{AB}=? \\ $$
Answered by A5T last updated on 19/Apr/24
Commented by A5T last updated on 19/Apr/24
$$\frac{{O}_{\mathrm{3}} {C}=\mathrm{1}}{{O}_{\mathrm{2}} {D}}=\frac{{O}_{\mathrm{3}} {O}}{{O}_{\mathrm{2}} {O}}=\frac{\mathrm{5}}{\mathrm{3}}\Rightarrow{O}_{\mathrm{2}} {D}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${AD}=\sqrt{{O}_{\mathrm{2}} {A}^{\mathrm{2}} −{O}_{\mathrm{2}} {D}^{\mathrm{2}} }=\sqrt{\mathrm{1}−\frac{\mathrm{9}}{\mathrm{25}}}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\Rightarrow{AB}=\mathrm{2}{AD}=\frac{\mathrm{8}}{\mathrm{5}}=\mathrm{1}.\mathrm{6} \\ $$
Commented by mr W last updated on 19/Apr/24
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