∵sinA/a=sinB/b=sinC/c=1/(2R)∴sinA=2sinBcosC===>a=2bcosC===>a/2=bcosC(AD⊥BC,BD=CD)∴b=c(等腰三角形三线合一)sin^2A=sin^2B+sin^2C====>a²=b²+c²====>∠A=90º∴△ABC为等腰直角三角形...