Let ABC be a triangle and P be an interior point. Prove that AB + AC + CA < 2 (PA+PB+PC)
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Given : ABC is a triangle where p is interior point.
To prove : AC+BC>AP+BP
Proof : In triangle ABC
angle A > angle PAB [ Whole is greater than a part ] ____(1)
angle B > angle PBA [ Whole is greater than a part ] _____(2)
On adding (1) and (2) we get
angle A + angle B > angle PAB + angle PBA
BC + AC > PB + AP [ Side opp. to respective angles ]
Or
AC + BC > AP + PB
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