a/sinA=b/sinB=c/sinC=k=>a=ksinA,b=ksinB,c=ksinC=>a+b+c=ksinA+ksinB+ksinC=k(sinA+sinB+sinC)=>(a+b+c)/(sinA+sinB+sinC)=k(sinA+sinB+sinC)/(sinA+sinB+sinC)=k=a/sinA=b/sinB=c/sinC
