作等边△ABC的三条高AD、BE、CF,相交于点O.
则点O是△ABC的外接圆圆心,也是内接圆圆心,
且有：R = OA ,r = OD .
BO是△ABD的角平分线,且 BD = (1/2)BC = (1/2)AB ；
可得：R∶r = AO∶OD = AB∶BD = 2∶1 ,
即有：R = 2r .