Question 103
Let $AD$, $BE$ and $CF$ Be the Angle Bisectors in a Triangle $ABC$, and let $I$ Be their intersection point. The Perpendicular Bisector of Segment $AD$ intersects lines $BE$ and $CF$ at points $M$ and $N$, respectively. Prove that the points $A$, $I$, $M$, and $N$ are concyclic. (D. prokopenko) in a triangle $ABC$ Bisectors were carried out $AD, BE$ and $CF$intersecting at a point $I$. middle perpendicular to the segment $AD$ Crosses straight lines $BE$ and $CF$ at points $M$ and $N$ respectively. Prove that points $A, I, M$ and $N$ lie on the same circle. (D. Prokopenko)