Consider a circle with diameter $AB$ and let $C,D$ be points on its circumcircle such that $C,D$ are not in the same side of $AB$.Consider the parallel line to $AC$ passing from $D$ and let it intersect $AB$ at $E$.Similarly consider the paralell line to $AD$ passing from $C$ and let it intersect $AB$ at $F$.The perpendicular line to $AB$ at $E$ intersects $BC$ at $X$ and the perpendicular line to $AB$ at $F$ intersects $DB$ at $Y$.Prove that the permiter of triangle $AXY$ is twice $CD$. Remark:This problem is proved to be wrong due to a typo in the exam papers you can find the correct version here.