G4.4 In Figure $1, \triangle A B C$ is an isosceles triangle, $A B=B C=20 \mathrm{~cm}$ and $\tan \angle B A C=\frac{4}{3}$. If the length of radius of the inscribed circle of $\triangle A B C$ is $r \mathrm{~cm}$, find the value of $r$.
$$
\angle B A C=\angle B C A ; \sin \angle B A C=\frac{4}{5}, \cos \angle B A C=\frac{3}{5} .
$$
$A C=2 \times 20 \cos \angle B A C=40 \times \frac{3}{5}=24$, the height of $\triangle A B C$ from $B=20 \sin \angle B A C=16$
Area of $\triangle A B C=\frac{1}{2} \cdot 24 \cdot 16=192=\frac{r}{2}(20+20+24)$
$$
r=6
$$