Radius R=?

the triangle above is Isosceles so the hypotenuse is $(5-x)\sqrt { 2 }$

$(5-x)\sqrt { 2 } = (5+x)$

$x=15-10 \sqrt { 2 }$

so,

5sin45+Rsin45+R=5

5(0.707)+R(0.707+1)=5

R(1.707)=5-3.53

R=1.47/1.707

R=0.865 m