26. The circle inscribed in triangle $A B C$ divides the median $B M$ into three equal parts. Find the ratio of the sides $|B C|:|C A|:|A B|$.
26. Let the segments of the median have length $a$. Denote by $x$ the smaller of the segments into which the side corresponding to the median is divided by the point of tangency. Now all sides can be expressed in terms of $a$ and $x$. The sides enclosing the median: $a \sqrt{2}+x$, $3 a \sqrt{2}+x$, the third side: $2 a \sqrt{2}+2 x$. Using the formula for the length of the median, we get

$$
9 a^{2}=\frac{2(a \sqrt{2}+x)^{2}+2(3 a \sqrt{2}+x)^{2}-(2 a \sqrt{\overline{2}}+2 x)^{2}}{4},
$$

from which $x=\frac{a \sqrt{\overline{2}}}{4}$.

Answer: $10: 5: 13$.