Question 54
Let $ABC$ be a triangle, let $I$ be its incenter, let $\Omega$ be its circumcircle, and let $\omega$ be the circle tangent to the sides $AB$ and $AC$, and internally tangent to $\Omega$. Let $D, E$ and $T$ be the points of contact of $\omega$ and $AB, AC$ and $\Omega$, respectively, let the line $IT$ cross $\omega$ again at $P$, and let the lines $PD$ and $PE$ cross the line $BC$ at $M$ and $N$ respectively. Prove that the points $D, E, M, N$ lie on a circle. What is the center of this circle?
Severius Moldovan
Severius Moldovan