Question

If D is any point on the side BC of a ∆ABC, then: (A) AB + BC + CA > 2AD (B) AB + BC + CA < 2AD (C) AB + BC + CA > 3AD (D) None

Answer 1

AB+BC+CA greater then 3AD

Answer 2

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