In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 8$,$AC = 10$ and $BD = 3.2$,then $DC = \ldots$

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 8$,$XZ = 6$ and $MZ = 4.8$,find $YZ$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$,$N \in \overline{AB}$ and $M \in \overline{BC}$. Prove that $AM^{2} + CN^{2} = AC^{2} + MN^{2}$.

In rhombus $ABCD$,$AC = 16$ and $BD = 30$. Find its perimeter.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 20$ and $BC = 21$,find $BM$. (in $.5$)

The correspondence $ABC \leftrightarrow QPR$ between $\Delta ABC$ and $\Delta PQR$ is a similarity. If $m \angle A : m \angle B : m \angle C = 15 : 8 : 7$,find the measures of all the angles of $\Delta PQR$.