ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that perimeter of triangle PQR is double the perimeter of triangle ABC.
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AB parallel to Qp and BC parallel to RQ so ABCQ is a parellogram
Similarly BCAR and ABPC are parellogram
BC=AQ and BC =RA
A is midpoint of QR
Similarly B and C are midpoint of PR and PQ respectively
AB=1/2 PQ ; BC =1/2 QR and CA=1/2 PR
PQ=2AB ; QR=2BC ; PR=2CA
Now perimeter of triangle PQR=PQ + QR+ PR
=2(AB+BC+CA)
=2 the perimeter of triangle ABC
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