Question

n figure,∆ABC is a right triangle and CN and AM are the medians.If AB=8cm and BC=5cm,then AM²+CN²= ​

Answer 1

Given: △ABC, ∠B=90∘

and BM is median AC

By Apollonius Theorem,

AB ^2 +BC ^2

=2(BM ^2 +MC ^2 )

8 ^2 +6 ^2

=2(BM ^2 +5 ^2 )

64+36=2(BM ^2 +25)

50=BM ^2 +25

BM ^2 =25

∴BM=5 cm