Question 1
Let the diagonals of the square $ABCD$ intersect at $S$ and let $P$ be the midpoint of $AB$. Let $M$ be the intersection of $AC$ and $PD$ and $N$ the intersection of $BD$ and $PC$. A circle is inscribed in the quadrilateral $PMSN$. Prove that the radius of the circle is $MP-MS$.