Let $S$ be the center of a square $ABCD$ and $P$ be the midpoint of $AB$. The lines $AC$ and $PD$ meet at $M$, and the lines $BD$ and $PC$ meet at $N$. Prove that the radius of the incircle of the quadrilateral $PMSN$ equals $MP-MS$.
Source: Croatia MO 2001 1st Grade P2
Tags: geometry, inradius
Let $S$ be the center of a square $ABCD$ and $P$ be the midpoint of $AB$. The lines $AC$ and $PD$ meet at $M$, and the lines $BD$ and $PC$ meet at $N$. Prove that the radius of the incircle of the quadrilateral $PMSN$ equals $MP-MS$.