Wyznacz r  (małe ) ze wzoru [latex] frac{2r sqrt{3}}{3} +r=R[/latex]

(2r√3+3r)/3=R (2√3 +3)r/3=R 3R=(2√3 +3)r 3R/(2√3 +3)=r

[latex]frac{2rsqrt{3}}{3}+r=R\2rsqrt{3}+3r=3R\r(2sqrt{3}+3)=3R\r=frac{3R}{2sqrt{3}+3}\r=frac{3R(2sqrt{3}-3)}{(2sqrt{3}+3)(2sqrt{3}-3)}\r=frac{3R(2sqrt{3}-3)}{12-9}\r=frac{3R(2sqrt{3}-3)}{3}\r=R(2sqrt{3}+3)[/latex]