In $\Delta XYZ$,$\overline{XN}$ is a median. If $XY^2 + XZ^2 = 200$ and $XN = 8$,find $YZ$.

In $\Delta ABC$, $P$ and $Q$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta APQ = 12 \sqrt{3}$, then the area of $\Delta ABC = \ldots$ (in $\sqrt{3}$)

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 6$ and $AC = 10$,find the area of $\Delta ABC$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle Q$. If $\frac{AB}{PQ} = \frac{4}{5}$ and $AC = 20$,find $PR$.

In the figure,if $\angle ACB = \angle CDA$,$AC = 8 \, cm$ and $AD = 3 \, cm$,find $BD$ (in $cm$).

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 15$,$QS = 10$,and $SR = 8$,then $PR = $.........