In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 8$,$MB = 12$ and $MC = 6$,find $MD$.

In rhombus $ABCD$,$AC = 24$ and $BD = 70$. Find the perimeter of rhombus $ABCD$.

$A$ flag pole $18 \, m$ high casts a shadow $9.6 \, m$ long. Find the distance of the top of the pole from the far end of the shadow. (in $m$)

In $\Delta PQR$, the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 5$, $QS = 4$ and $QR = 9.6$, find $PR$.

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect at $O$. $\overrightarrow{AO}$ intersects $\overline{BC}$ at $P$. Prove that $\frac{AB}{AC} = \frac{BP}{PC}$.

In $\Delta ABC$,$\overline{AD}$ is a median. The bisectors of $\angle ADB$ and $\angle ADC$ intersect $\overline{AB}$ and $\overline{AC}$ at $E$ and $F$ respectively. Prove that $\overline{EF} \parallel \overline{BC}$.