Question

In ∆ABC if M is the midpoint of side BC then find AB²+AC² = 2AM² +2BM²​

Answer 1

Step-by-step explanation:

△ABC, point M is the midpoint of side BC

 BM=MC=21BC

AB2+AC2=2AM2+2BM2 (by Apollonius theorem)

⇒290=2(8)2+2BM2

⇒290=128+2BM2

⇒2BM2=162

⇒BM2=81

⇒BM=9

∴BC=2×BM

=2×9

=18cm 

Hence, BC=18 cm