In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $AC = 14\sqrt{2}$. If $AB = BC$,find the area of $\Delta ABC$.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides,then the two sides are divided in the same ratio.

In $Fig.$,line segment $DF$ intersects the side $AC$ of a triangle $ABC$ at the point $E$ such that $E$ is the mid-point of $CA$ and $\angle AEF = \angle AFE$. Prove that
$\frac{BD}{CD} = \frac{BF}{CE}$

$A$ line drawn parallel to $\overline{YZ}$ in the plane of $\Delta XYZ$ passes through the midpoint of $\overline{XY}$. Prove that this line bisects $\overline{XZ}$.

In $\Delta ABC$,$D$ and $E$ are the midpoints of $\overline{BC}$ and $\overline{AC}$ respectively. $\overline{AD}$ and $\overline{BE}$ intersect at $G$. Line $m$ passing through $D$ and parallel to $\overline{BE}$ intersects $\overline{AC}$ at $K$. Then,$AC = \ldots$ (in $EK$)

In $\Delta ABC$,$m \angle A = 90^{\circ}$. If $a = 20$ and $b = 12$,then $c = \dots$