Question 121
Let $ABC$ be an acute-angled triangle and $W$ the intersection point of the bisector of $\angle ACB$ with the side $AB$. Furthermore, let $I_{A}$ and $I_{B}$ be the incentres of the triangles $AWC$ and $WBC$ respectively. The lines $I_{A}W$ and $I_{B}B$ intersect at the point $D$. Let $M$ be the midpoint of the segment $DI_{B}$. Show that $MWBC$ is a cyclic quadrilateral.
Remark: The three angle bisectors of a triangle meet in a point, the incentre.
Remark: The three angle bisectors of a triangle meet in a point, the incentre.