(a+b+c)/(sinA+sinB+sinC)=2R
问题描述:
(a+b+c)/(sinA+sinB+sinC)=2R
怎么证明?
答
正弦定理:a/sinA=b/sinB=c/sinC=2R
(a+b+c)/(sinA+sinB+sinC)=(2R sinA+2R sinB+2RsinC)/(sinA+sinB+sinC)
=2R (sinA+sinB+sinC)/(sinA+sinB+sinC)
=2R