In $\Delta XYZ,$ the bisector of $\angle X$ intersects $\overline{YZ}$ at $T$. If $XY = 10, XZ = 14$ and $YT = 5,$ find $YZ.$

In $\Delta ABC$,$m\angle B = 90^{\circ}$,$AB = 2x + 3$,$BC = x + 2$,and $AC = 3x - 1$. Find the value of $x$.

$\Delta DEF \sim \Delta PQR$ for the correspondence $DEF \leftrightarrow QPR$. If $2 DE = 3 PQ$ and $QR = 8$,then $DF = \ldots$

$\square XYZW$ is a rectangle. If $XY + YZ = 17$ and $XZ + YW = 26$,find $XY$ and $YZ$ (given $XY > YZ$).

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 10$,$BC = 6$,and $AC = 14$,find $BD$ and $DC$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $\frac{AB}{CD} = \frac{2}{1}$ and $AC = 15$,find $MA$ and $MC$.