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Question
In ABC, P, Q and R are points on AB, BC and AC respectively. Prove that AB + BC + AC > PQ + QR + PR.
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Solution
In triangle APR,
AP + AR > PR ......(i)
In triangle BPQ,
BQ + PB > PQ .......(ii)
In triangle QCR,
QC + CR > QR .......(iii)
Adding (i), (ii) and (iii)
AP + AR + BQ + PB + QC + CR > PR + PQ + QR
(AP + PB) + (BQ + QC) + (CR + AR) > PR + QR + PQ)
⇒ AB + BC + AC > PQ + QR + PR.
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