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inradius of PMSN equals to MP-MS (Singapore Junior 2010)

Source:

July 11, 2019
geometryinradiussquaretangential

Problem Statement

Let the diagonals of the square ABCDABCD intersect at SS and let PP be the midpoint of ABAB. Let MM be the intersection of ACAC and PDPD and NN the intersection of BDBD and PCPC. A circle is incribed in the quadrilateral PMSNPMSN. Prove that the radius of the circle is MPāˆ’MSMP- MS.
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