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