Question

In ABC, P, Q and R are points on AB, BC and AC respectively. Prove that AB + BC + AC > PQ + QR  + PR.

Answer 1

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.