D为三角形ABC内一点,且AB^2-AC^2=DB^2+DC^2 证AD垂直BC

题目错误,只有AB^2-AC^2=DB^2-DC^2时,才有AD⊥BC.以下按照新题目证明.过A做AP⊥BC于P,过D做DQ⊥BC于Q.那么根据勾股定理,AB^2-AC^2=(AP^2+PB^2)-(AC^2+PC^2)=PB^2-PC^2=PB^2-(BC-PB)^2=2BC*BP-BC^2.同理DB^2-DC^2=(DQ...