Q27 of 168 Page 4

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.

More from this chapter

All 168 →
25

If ABC is an isosceles triangle and D is a point on BC such that, then

 26

is a right triangle right-angled at A and . Then, =

 28

If E is a point on side CA of an equilateral triangle ABC such that, then AB2 + BC + CA2 =

 29

In a right triangle ABC right-angled at B, if P and Q are points on the sides AB and AC respectively, then