In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 6$,$MB = 12$ and $AN = 8$,find $AC$.

In $\Delta ABC$ and $\Delta XYZ$,$\angle A \cong \angle Y$ and $\angle B \cong \angle Z$. If $\frac{AC}{YX} = \frac{5}{7}$ and $AB = 7$,find $YZ$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $\overline{AC}$. If $BD = 2CD$,prove that $AC = 5CD$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 11$ and $BC = 60$,find the perimeter of $\Delta ABC$.

In $\Delta ABC$,$\Delta PQR$,and $\Delta XYZ$,the correspondences $ABC \leftrightarrow QPR$ and $PQR \leftrightarrow YZX$ are similarities. Then,the correspondence $ABC \leftrightarrow \dots$ is a similarity.

In $\Delta PQR$,$P-X-Q$,$P-Y-R$ and $\overline{XY} \parallel \overline{QR}$. If $PY = 4$,$YR = 7$ and $XY = 11$,find $QR$.