Question

In Figure-4, BN and CM are medians of a triangle ABC right-angled at A. Prove
that 4 (BN² + CM²) = 5 BC²

please solve this question ​

Answer 1

Step-by-step explanation:

We have,

✓ 4( BN² + CM² ) = 4( ( AB² + AN² ) + ( AC² + AM² ) )

= 4( AB² + AC² + ( AB / 2 )² + ( AC / 2 )² )

= 4( BC² + 0.25( AB² + AC² ) )

= 4( 1.25 BC² )

= 5BC²

✓✓ Proved ✓✓