13. Given the sides $a, b, c$ of triangle $ABC$, find its angle bisectors. (O. 117, P. 181.)
13. Let's keep the notations from the previous problem. Since

$$
a_{1}=\frac{a c}{a+b}, \quad b_{1}=\frac{b c}{a+b}
$$

Then

$$
C C_{1}^{2}=a h-\frac{a b c^{2}}{(a+b)^{2}}, \text{ or } C C_{1}^{2}=a b\left[1-\frac{c^{2}}{(a+b)^{2}}\right]
$$

We could slightly modify the solution to the problem by placing masses of $a$ and $b$ units in $A$ and $B$ respectively.