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Question
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) =
Options
4 AC2
5 AC2
- \[\frac{5}{4} {AC}^2\]
6 AC2
Solution
M is the mid-point of AB.
∴ \[BM = \frac{AB}{2}\]
N is the mid-point of BC.
∴\[BN = \frac{BC}{2}\]
Now,
`AN^2+CM^2=(AB^2+(BC)^2)+((AB)^2+BC^2)`
`=AB^2+BC^2+1/4AB^2+BC^2`
`=5/4(AB^2+BC^2)`
`⇒ 4(AN^2+CM^2)=5AC^2`
Hence option (b) is correct.
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