Question 24
Let $ABC$ be a triangle with incenter $I$; the bisectors of the angles at $C$ and $B$ meet $AB$, $AC$ at $D$, $E$ respectively. Denote by $\Delta_{b}$, $\Delta_{c}$ the lines symmetric to the lines $AB$, $AC$ with respect to $CD$, $BE$ correspondingly. Suppose that $\Delta_{b}$, $\Delta_{c}$ meet at $K$.
1. Prove that $IK \perp BC$.
2. If $I \in (KDE)$, prove that $BD + CE = BC$.
1. Prove that $IK \perp BC$.
2. If $I \in (KDE)$, prove that $BD + CE = BC$.