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) =

पर्याय

• 4 AC²

•  5 AC²

• \[\frac{5}{4} {AC}^2\]

• 6 AC²

Answer 1

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.