The Insphere is not necessarily a tangent at the circumference of the faces of a dual polyhedron but is rather an only tangent at some point which lies on the face. The below section provides you the insphere radius of octahedron formula to calculate the inradius on your own. To find inradius just find the product of edge length and the square root of 6 and divide the resultant value by 6. The square root of 6 is 2.449, so you can directly use this value in the formula for calculation.
Also, you can navigate to the useful online calculator which works based on the Insphere radius of octahedron formula by just clicking on the tab in the related calculator section to make your calculations even more simple.