Question

已知三角形ABC中,AB=6,AC=9,AD垂直BC于D,M为AD上任一点,则MC的平方—MB的平方等于多少?

Answer 1

45

MD^2+CD^2=CM^2

MD^2+BD^2=BM^2

CM^2-BM^2=CD^2-BD^2

AC^2=AD^2+CD^2

AB^2=AD^2+BD^2

CD^2-BD^2=AC^2-AB^2=9*9-6*6=45

CM^2-BM^2=45