因AB>AC,AD垂直BC,故,BD>DC因,AD分三角形ABC为两个直角三角形：△ADB和△ADCAD^2=AB^2-BD^2AD^2=AC^2-DC^2故,AB^2-BD^2=AC^2-DC^2AB^2-AC^2=BD^2-DC^2=(BD+DC)*(BD-DC)=BC*(BD-DC)故,AB^2-AC^2=BC*(BD-DC)证毕....