There is a right triangle $ABC$ with right angle at $A$. Let the incircle touch $AB$ and $AC$ at $D$ and $E$, respectively. $X$ and $Y$ are the arc midpoints of minor arc $AB$ and $AC$ on $(ABC)$. Show that $X,Y,D,E$ collinear.
The lemma above is a step in in proving a different result which won’t be provided here. I am sure there will be an easy proof to the above, but I appear to be having difficulty in showing that it is true. Sorry for the lack of information about what I have already tried, but indeed I have not made too much progress; thanks in advance.