Question

AX, BY and CZ are the medians of $\Delta ABC$ intersecting at O. If CK is drawn parallel to BY to meet AX in K, then AO is

• A. $\frac{1}{4}AK$
• B. $\frac{1}{2}AK$
• C. $\frac{1}{3}AK$
• D. $\frac{2}{3}AK$

Answer 1

The correct option is B $\frac{1}{2}AK$

Since angles $BXO$ and $C$ are similar.
$\therefore$ $\frac{OX}{XK}=\frac{BX}{OX}=1$
$\Rightarrow$ $OX=XK$
Also,$\frac{AO}{XK}=\frac{AO}{OX}=\frac{2}{1}$
$\Rightarrow$ $AO=OK$
Hence, $AK=2AO$
$\Rightarrow$ $AO=\frac{1}{2}AK$