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BL and CM are medians of a triangle ABC...

BL and CM are medians of a triangle ABC right angled at A. Prove that `4(B L^2+C M^2)=5B C^2`

Text Solution

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Please refer to diagram in video.
As `BL` and `CM` are median to `AC` and `AB`.
So, `AM = BM = 1/2AB`
and `CL = AL = 1/2CA`
Now, in `Delta ABL`,
`BL^2 = AL^2+AB^2`
`BL^2 = ((AC)/2)^2+AB^2 = (AC^2)/4+AB^2`
`=>4BL^2 = AC^2+4AB^2->(1)`
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