Question

AD is the median of any ∆ABC. Is it true to say that AB + BC + CA > 2AD. Give reason for your answer.

Answer 1

Yes, if AD is median of ∆ABC

⇒ AB + BD > AD …(i) (sum of any two sides of a A is greater than third side)

and AC + DC > AD …(iii) (reason as above)

⇒ AB + (BD + DC) + AC > 2 AD

⇒ AB + BC + CA > 2AD