In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $a = 9$ and $c = 12$,then $b = \dots$

In $\Delta ABC,$ the bisectors of $\angle B$ and $\angle C$ intersect $\overline{AC}$ and $\overline{AB}$ at $D$ and $E$ respectively. If $\overline{DE} \parallel \overline{BC},$ prove that $\Delta ABC$ is an isosceles triangle.

In $\Delta ABC$,medians $\overline{AD}$ and $\overline{BE}$ intersect at $G$. $A$ line through $G$ and parallel to $\overline{DE}$ intersects $\overline{AC}$ at $K$. If $EK = 1.8$,then $AC = \ldots$

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

The heights of two poles standing erect on a flat ground are $6 \, m$ and $11 \, m$. If the distance between their bases is $12 \, m$,find the distance between their tops.

In the given figure,$\angle ADE = \angle AED$ and $\frac{AD}{DB} = \frac{AE}{EC}$. Prove that $\triangle ABC$ is an isosceles triangle.