Answer :

Given:- ΔABC and AD is median

To Prove:- AB2 + AC2 = 2(AD2 + CD2)



Proof:- Let, A at origin


be position vector of B and C respectively


Therefore,



Now position vector of D, mid-point of BC i.e divides BC in 1:1.


Section formula of internal division: Theorem given below


Let A and B be two points with position vectors


respectively, and c be a point dividing AB internally in the ration m:n. Then the position vector of c is given by


Position vector of D is given by



Now distance/length of CD


= position vector of D-position vector of C




Now taking RHS


= 2(AD2 + CD2)


=


=


=


=


=


= AB2 + AC2


= LHS


Hence proved

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