Question

State true or false:

In triangle $ABC$, $P$ is the mid-point of side $BC$. A line through $P$ and Parallel to $CA$ meets $AB$ at point $Q$; and a line through $Q$ and parallel to $BC$ meets median $AP$ at point $R$. Can it be concluded that, $BC=4QP$

• A. True
• B. False

Answer 1

The correct option is B False

Given: $△ABC$, P is mid point of BC, $QR\parallel BC$ and $PQ\parallel AC$
Since, $PQ\parallel AC$ and P is mid point of BC, thus, by converse of mid point theorem
Q is mid point of AB.
Now, In $△ABP$
Since, $QR\parallel BP$ and Q is mid point of AB. thus, by converse of Mid point theorem
R is mid point of AP.
Hence, $QR=\frac{1}{2}BP$ (Mid point theorem)
$QR=\frac{1}{2}\left(\frac{1}{2}BC\right)$ (P is midpoint of BC)
$BC=4QR$