Question 19
Let $ABC$ a triangle and $\omega$ his circle inscribed. we note $P, Q, R$ the contact points of $\omega$ with $(BC), (CA)$ and $(AB)$. A circle passing through $B$ and $C$ is tangent in $X$ à $\omega$, a circle passing through $C$ and $A$ is tangent in $Y$ à $\omega$ and a circle passing through $A$ and $B$ is tangent in $Z$ à $\omega$. Show that the lines $(PX), (QY)$ and $(RZ)$ are concurrent.