Question

If D is any point on the side BC of triangle ABC. Show that AB+BC+CA>2AD.​

Answer 1

Answer:

In ABD , By Inequality property of triangle

AB + BD > AD ----------(1)

And In ACD ,By Inequality property of triangle

DC + AC > AD ---------(2)

On Adding Eq (1) and Eq (2)

AB+BD+DC+AC> AD+AD

AB + BC + AC > 2 AD [Given BD+DC = BC]

 AB + BC + AC > 2 AD

hence Proved