Question Number 28518 by beh.i83417@gmail.com last updated on 26/Jan/18
Commented by beh.i83417@gmail.com last updated on 26/Jan/18
$$\boldsymbol{{all}}\:\boldsymbol{{radii}}=\mathrm{1},\:\boldsymbol{{ab}}=? \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{radius}}\:\boldsymbol{{of}}\:\boldsymbol{{a}}\:\boldsymbol{{circle}}\left({or}\:{circles}\right)\:\boldsymbol{{that}} \\ $$$$\boldsymbol{{tangents}}\:\boldsymbol{{to}}\:\boldsymbol{{this}}\:\mathrm{3}\:\boldsymbol{{circles}}. \\ $$
Commented by mrW2 last updated on 26/Jan/18
$${ab}={r}=\mathrm{1} \\ $$
Answered by mrW2 last updated on 27/Jan/18
Commented by mrW2 last updated on 27/Jan/18
$${big}\:{circle}: \\ $$$${R}_{\mathrm{1}} ={r}+\frac{\mathrm{2}}{\mathrm{3}}×\sqrt{\mathrm{3}}{r}=\left(\mathrm{1}+\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}}\right){r}\approx\mathrm{2}.\mathrm{15} \\ $$$$ \\ $$$${small}\:{circle}: \\ $$$${R}_{\mathrm{2}} =\frac{\mathrm{2}}{\mathrm{3}}×\sqrt{\mathrm{3}}{r}−\mathrm{1}=\left(\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}}−\mathrm{1}\right){r}\approx\mathrm{0}.\mathrm{15} \\ $$