ABC is a right triangle with legs a and b and hypotenuse c. Two circles of radius r are placed inside the triangle, the first tangent to a and c, the second tangent to b and c, and both circles externally tangent to each other. Draw a third circle of radius s tangent externally to the first two circles, and to the hypotenuse. What is the smallest possible radius of the third circle if a, b, c, r and s are distinct integers?