To find the radius you need to use,
1)Draw an Isoseles triangles with 13 13 and 10.
2)From the vertex drop a perpendicular to base side.
3)The base will be bisected and now length 5.
4)The height will be, by Pythagorean theorem 12.
Now the cosine of half the vertex angle is,
Thus, by half-angle identity,
Using the extended law of sines,