Question

D is a point on side BC of triangle ABC, Prove that : AB+BC+CA>2AD.

Answer 1

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Answer 2

Given: Triangle ABC in which D is a point on BC

To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any
two sides of a triangle is
always greater than the
third side] ---- 1
In triangle ADC,
AC + DC > AD [because, the sum of any
two sides of a triangle is
always greater than the
third side] ---- 2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved