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In $\triangle P Q R, M$ is the mid-point of $Q R$ and $C$ is the mid-point of $P M$. If $Q C$ when extended meets $P R$ at $N$, then $\frac{|\overrightarrow{Q N}|}{|\overline{C N}|}=$
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The correct answer is:
4
We have,
$M$ is the mid-point of $Q R$.
$C$ is the mid-point of $P M$.
Draw $M O$ such that $M O$ is parallel to $C N$.
$\because N$ is the mid-point of $P O$
$$
\therefore \quad C N=\frac{1}{2} M O
$$
$M$ is the mid-point of $Q R$
$\therefore M O$ is parallel to $Q N$
$$
\begin{array}{rlrl}
\because & & M O & =\frac{1}{2} Q N \\
& \therefore & C N & =\frac{1}{2}\left(\frac{1}{2} Q N\right) C N=\frac{1}{4} Q N \\
\therefore & & \left|\frac{\mathbf{Q N}}{\mathbf{C N}}\right|=4 .
\end{array}
$$
$M$ is the mid-point of $Q R$.
$C$ is the mid-point of $P M$.
Draw $M O$ such that $M O$ is parallel to $C N$.
$\because N$ is the mid-point of $P O$
$$
\therefore \quad C N=\frac{1}{2} M O
$$
$M$ is the mid-point of $Q R$
$\therefore M O$ is parallel to $Q N$
$$
\begin{array}{rlrl}
\because & & M O & =\frac{1}{2} Q N \\
& \therefore & C N & =\frac{1}{2}\left(\frac{1}{2} Q N\right) C N=\frac{1}{4} Q N \\
\therefore & & \left|\frac{\mathbf{Q N}}{\mathbf{C N}}\right|=4 .
\end{array}
$$
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