Question 19
Let $ABC$ be a non-isosceles triangle. Let $\omega$ be its incircle and $I$ its center. Let $M, N, P$ be the points of tangency of $\omega$ with the sides $[BC], [CA], [AB]$. Let $J$ be the intersection point of $(MN)$ and $(IC)$. The line $(PJ)$ meets $\omega$ again at $K$. Show that
a) $CKIP$ is cyclic;
b) $(CI)$ is the bisector of $\widehat{PCK}$.
a) $CKIP$ is cyclic;
b) $(CI)$ is the bisector of $\widehat{PCK}$.