Question 14
Demonstrate that the necessary and sufficient condition so that, in the triangle $ABC$, the median from $B$ is divided into three equal parts by the circumference inscribed in the triangle, is
$$
\frac{a}{5}=\frac{b}{10}=\frac{c}{13}
$$
$$
\frac{a}{5}=\frac{b}{10}=\frac{c}{13}
$$