数形结合
建立xy坐标轴,令AB为x轴上任意两点(xA>xB),点C在y轴上,
S△=(a+b+c)R/2
R=ch/(a+b+c)=|AB|·y/(xA-xB+√(xA²+y²)+√(xB²+y²))=f(y)
f'(y) =
|AB|[1·(xA-xB+√(xA²+y²)+√(xB²+y²)) - y·(y/√(xA²+y²)+y/√(xB²+y²))]
=|AB|[xA-xB+XA²/√(xA²+y²) + xB²/√(xB²+y²))]>0恒成立
建立xy坐标轴,令AB为x轴上任意两点(xA>xB),点C在y轴上,
S△=(a+b+c)R/2
R=ch/(a+b+c)=|AB|·y/(xA-xB+√(xA²+y²)+√(xB²+y²))=f(y)
f'(y) =
|AB|[1·(xA-xB+√(xA²+y²)+√(xB²+y²)) - y·(y/√(xA²+y²)+y/√(xB²+y²))]
=|AB|[xA-xB+XA²/√(xA²+y²) + xB²/√(xB²+y²))]>0恒成立