Answer :
The proof is as follows :
Step-by-step explanation:
Let NC = x
⇒ AB = 3x and AN = 2x
In Δ ABN, By using Pythagoras theorem,
AB² = BN² + AN²
⇒ BN² = AB² - AN²
⇒ BN² = (3x)² - (2x)²
⇒ BN² = 5x²
⇒ BN = x√5 .......................(1)
Now in ΔANC , Using Pythagoras theorem We have,
AC² = NC² + AN²
⇒ AC² = x² + (2x)²
⇒ AC² = 5x²
⇒ AC = x√5 ....................(2)
From equations (1) and (2) We get,
AC = BN , which is our required result
