AB-BD=AC-CD
AD/sin∠B-AD/tg∠B=AD/sin∠C-AD/tg∠C
(1-cos∠B)/sin∠B=(1-cos∠C)/sin∠C
tg(∠B/2)=tg(∠C/2)
∠B=∠C
△ABC是等腰三角形