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Question

Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ΔABC as shown in figure. Show that BC=12QR.

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Solution

Given in ΔABC, PQ ∥ AB and PR ∥ AC and RQ ∥ BC

To show BC=12QR.

Proof in Quadrilateral BCAR, BR ∥CA and BC ∥ RA

So, quadrilateral , BCAR is a parallelogram.

BC=AR ….(i)

Now, in quadrilateral BCQA, BC ∥AQ

And AB ∥ QC

So, quadrilateral BCQA is a parallelogram.

BC = AQ …..(ii)

On adding Eqs (i) and (ii) we get

2BC = AR + AQ

2BC=RQ

BC=12QR. Hence proved

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