Question

已知如图所示,在△ABC中∠C=90°,AD是BC边上的中线,DE⊥AB于E.求证AC平方=AE平方－BE平方

Answer 1

AC^2=AD^2-DC^2

AD^2=AE^2+ED^2

ED^2=BD^2-EB^2 BD^2=DC^2

则AC^2=AD^2-DC^2=AE^2+ED^2-DC^2=AE^+BD^2-EB^2-DC^2=AE^-EB^2