my problem is the following.
A triangle ABC is given. P is a point on $\overline{AB}$. $k_1, k_2, k$ are the radii of the in-circles of APC, BPC, ABC. $s_1, s_2, s$ are radii of the ex-circles of these triangles which are lying at the angle ACB.
Show that \begin{equation} \frac{k_1}{s_1} \cdot \frac{k_2}{s_2} = \frac{k}{s} \end{equation}
Hope you can help me.
Thanks.