Question

A $\Delta ABC$ is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming $\Delta PQR$, as shown in the adjoining figure, show that $BC=\frac{1}{2}QR$.

Answer 1

Solution :
$BC\parallel QAandCA\parallel QB$
i.e., BCQA is a parallelogram.
$\therefore BC=QA$
...(i)
Similarly, $BC\parallel ARandABparallelCR$
i.e., BCRA is a parallelogram.
$\therefore BC=AR$ ...(ii)
But QR = QA + AR
From (i) and (ii), we get:
QR = BC + BC
$\to QR=2\times BC$ ​
$\therefore BC=12\times QR$