In triangle PQR, a line XY parallel to QR cuts PQ at X and PR at Y in which PX/XQ=PY/YR=1/2.Then

a)XY=QR

b)XY=1/2QR

Question

In triangle PQR, a line XY parallel to QR cuts PQ at X and PR at
Y in which PX/XQ=PY/YR=1/2 Then
a)XY=QR
b)XY=1/2QR

Pronay · Accepted Answer

Consider Î”PQR and Î”PXY âˆ PQR=âˆ PXY ( corresponding angles and XY is parallel to QR) âˆ QPR= âˆ XPY (common) Therefore Î”PQRâˆ¼Î”PXY This implies $\frac{PX}{PQ} = \frac{PY}{PR} = \frac{QR}{XY} \Rightarrow \frac{PX}{PQ - PX} = \frac{PY}{PR - PY} = \frac{QR}{XY - QR} \Rightarrow \frac{PX}{XQ} = \frac{PY}{YR} = \frac{QR}{XY - QR} \Rightarrow \frac{QR}{XY - QR} = \frac{1}{2} \Rightarrow 2 QR=XY - QR \Rightarrow 3 QR=XY \Rightarrow \frac{QR}{XY} = \frac{1}{3} \Rightarrow XY=3 QR$

In triangle PQR, a line XY parallel to QR cuts PQ at X and PR at Y in which PX/XQ=PY/YR=1/2.Then a)XY=QR b)XY=1/2QR

In triangle PQR, a line XY parallel to QR cuts PQ at X and PR at Y in which PX/XQ=PY/YR=1/2.Then

a)XY=QR

b)XY=1/2QR