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) =

(a) 4 AC²
(b) 5 AC²
(c) $\frac{5}{4}{\mathrm{AC}}^2$
(d) 6 AC²

Answer 1

M is the mid-point of AB.

∴ $\mathrm{BM}=\frac{\mathrm{AB}}{2}$

N is the mid-point of BC.

∴ $\mathrm{BN}=\frac{\mathrm{BC}}{2}$

Now,

Hence option (b) is correct.