If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4 (AN2 + CM2) =
Given ABC is a right triangle right-angled at B and M, N are mid-points of AB and BC respectively.
M is the mid-point of AB.
And N is the mid-point of BC.
Now,
⇒ AN2 + CM2 = (AB2 + ( �BC)2) + (( �AB)2 + BC2)
= AB2 + �BC2 + 1/4 AB2 + BC2
= 5/4 (AB2 + BC2)
∴ 4 (AN2 + CM2) = 5AC2
Hence proved.
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