Triangle Properties with Circumcircle

In a right triangle ABC, where angle C is the right angle, the lengths of the legs AC and BC are represented as x and y, respectively. Triangle ABC is inscribed in a circle (circumcircle) with radius r. The area A of triangle ABC can be expressed in terms of its legs as:

$$A = rac{1}{2}xy$$

Furthermore, the radius of the circumcircle of a right triangle can be calculated using the formula:

$$r = rac{c}{2}$$

where c is the hypotenuse. If the hypotenuse is given by:

$$c = ext{sqrt}(x^2 + y^2)$$

Given that the area of triangle ABC is 24 square units, express x in terms of y and the radius r such that 0 <= y < 10. Use this relation to find the value of x when r equals 10 and y equals 8. Then round to the nearest hundredth.