Q. 113.9( 43 Votes )

# In <span lang="EN

Answer :

We know, By Apollonius theorem

In ΔABC, if L is the midpoint of side AC, then AB2 + BC2 = 2BL2 + 2AL 2

Given that, BL is median i.e. L is the mid-point of CA AB2 + BC2 = 2BL2 + 2AL2  Also, if M is the midpoint of side AB, then AC2 + BC2 =2CM2 + 2BM2

Given that, CM is median i.e. M is the mid-point of BA AC2 + BC2 = 2CM2 + 2BM2  Also, In ΔABC, By Pythagoras theorem i.e.

(Hypotenuse)2 = (base)2 + (Perpendicular)2

BC2 = AC2 + AB2 

Adding  and  AB2 + AC2 + 4BC2 = 4(BL2 + CM2)

BC2 + 4BC2 = 4(BL2+ CM2) [From 3]

5BC2 = 4(BL2+ CM2)

Hence Proved.

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