You can find the radius of the small circle by constructing a suitable right angled triangle. Let A be the center of the small circle, B the center of either large circle and C the point where the large circles touch. The lines AC and BC are perpendicular, so triangle ABC is right angled and you can apply the Pythagorean theorem. The length of the line segment AB is equal to the sum of the radii, the length of the line segment AC is equal to the difference of the radii and the length of BC is the radius of the larger circle. This gives you an equation for the radius of the smaller circle in terms of the radius of the larger circle.