Question 2
Let $P$ be a point inside $\triangle ABC$ such that
$$\angle APB-\angle C=\angle APC-\angle B.$$
Let $D,E$ be the incenters of $\triangle APB,\triangle APC$ respectively. Show that $AP$, $BD$, and $CE$ meet in a point.
$$\angle APB-\angle C=\angle APC-\angle B.$$
Let $D,E$ be the incenters of $\triangle APB,\triangle APC$ respectively. Show that $AP$, $BD$, and $CE$ meet in a point.