Question 3
(SPA 1) Consider the triangle $ABC$, its circumcircle $k$ with center $O$ and radius $R$, and its incircle with center $I$ and radius $r$. Another circle $k_c$ is tangent to the sides $CA,CB$ at $D,E$, respectively, and it is internally tangent to $k$.
Show that the incenter $I$ is the midpoint of $DE$.
Show that the incenter $I$ is the midpoint of $DE$.