In a triangleABC,AD is a median on BC&AE is perpendicular toBC.Prove thtAB.AB=AD.AD-BC.DE+1/4BC.BC

 

 

 

 

                          

Given:-In the adjoining figure D is mid point of side BC of Triangle ABC and AD is the median from A to side BC .and AE is the perpendicular drawn from A to BC.

 

To Prove:-AB² = AD² – BC.DE + ¼ BC²   

 

Proof:- AB² = AE² + BE²

            AB² = AD² – ED² + (BD –ED)²

            AB² = AD² – ED² + BD² + ED² -2*BD*ED

            AB² = AD² – 2*BC/2 * DE + (1/2 BC)²

            AB² = AD² – BC * DE + 1/4 BC²