Pre-RMO 2015

Geometry Level 4

A square PQRS length of its side equal to 3+āˆš5. LetM be the mid-point of the side RS. Also, let Cā‚ be the in-circle of triangle PMS and Cā‚‚ be the circle that touches the sides PQ, QR and PM. Find the radius of the circle Cā‚‚.

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