Prove that AC + BC = 2AB

Hey everyone,
I've got troubles solving this task, maybe you will be able to solve it (Nod)

Point P,Q,R lie adequately on sides BC, CA and AB of traingle ABC (as shown on the picture). We know that AR = RP = PC and BR = RQ = QC.
Prove that AC + BC= 2AB

My first idea was to prove it using vectors, but unfortunately I failed (Surprised)
I will try to prove it again, but maybe you will help me a bit
Thanks in advance!
Lukasz

Quote:

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Originally Posted by Lukaszm

Prove that AB + BC= 2AB Lukasz

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Do you mean to prove : BC = AB ?

Oups, there should be AC + BC = 2AB, sorry ;)