Question

已知△ABC内接于圆O,AB=AC,角BAC=120°,BC=12cm,则圆O的半径为多少

Answer 1

解；连接OA,与BC交于点M.OA=OC,又AB=AC,OB=OB所以△OAB全等于△OAC,所以角OAB=角OAC,又AB=AC,AM=AM,所以△MAB全等于△MAC,所以角AMB=角AMC,所以BM=CM;角AMB=角AMC=90°,所以AM垂直于BC,即0A垂直于BC.△OAB中角OAB=1/2×120°=60°,则角MOA=60°解△OAM,OA=r,0M垂直于OA,则OA=12/2×2/根下3=4倍根下3,即r=4倍根下3