[b]Let ABCD be a parallelogram. M and N are the midpoints of the sides BC and CD, respectively. Let Q be the intersection point of the lines AM and BN.[/b][br][b]Find the value of the ratio AQ/QM.[/b]
Construct through point M a line parallel to line CD and mark the intersection with BN with F.[br]Then FM is...
[math]\frac{NC}{2}=5[/math]
FM||AB [math]\Longrightarrow\Delta ABQ\sim......[/math]
[math]\frac{AQ}{QM}=................[/math]
[math]\frac{AB}{MF}=\frac{2NC}{MF}=\frac{4MF}{MF}=4[/math]