Question Number 27942 by beh.i83417@gmail.com last updated on 17/Jan/18
Commented by beh.i83417@gmail.com last updated on 17/Jan/18
$$\angle{A}=\mathrm{60}^{°} ,{AB}={c},{AC}={b},{BC}={a} \\ $$$${draw}\:{tangent}\:{lines}\:{from}:{B}\:{and}\:{C},{to}\:{circle}, \\ $$$${such}\:{that}:\angle{FBC}=\angle{FCB}. \\ $$$$\left.\mathrm{1}\right){find}\:{radius}\:\boldsymbol{{r}}\:{in}\:{terms}\:{of}:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}. \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{is}}\:{it}\:{possible}\:{for}:\angle{BFC}=\mathrm{90}^{\bullet\:} \:? \\ $$$$ \\ $$
Answered by ajfour last updated on 17/Jan/18
$$\left.\mathrm{1}\right)\:\boldsymbol{{r}}\:{is}\:{independent}\:{of}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:. \\ $$$$\left.\mathrm{2}\right)\:{yes}\:. \\ $$