Problem

Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade

Tags: geometry, equal angles, power of a point



The diagonals $AC$ and $BD$ of a convex quadrilateral $ABCD$ intersect in point $M$. The angle bisector of $\angle ACD$ intersects the ray $\overrightarrow{BA}$ in point $K$. If $MA.MC+MA.CD=MB.MD$, prove that $\angle BKC=\angle CDB$.