Question 89
Let $A A'$, $B B'$ and $C C'$ be the angular bisectors of a triangle $A B C$ with incenter $I$. The segments $C I$ and $A' B'$ meet at $D$ and the midpoints of the segments $A I$ and $B I$ are denoted by $M$ and $N$, respectively.
a) If $a = B C$, $b = A C$ and $c = A B$, find the ratio $C D : D I$.
b) If $K = A C \cap \overrightarrow{C' M}$ and $L = B C \cap \overrightarrow{C' N}$, prove that $D$ is the incenter of $\triangle K L C$.
a) If $a = B C$, $b = A C$ and $c = A B$, find the ratio $C D : D I$.
b) If $K = A C \cap \overrightarrow{C' M}$ and $L = B C \cap \overrightarrow{C' N}$, prove that $D$ is the incenter of $\triangle K L C$.