In a triangle the sum of two sides is x and the product of the same two sides is y. If $$x^2 - c^2 = y,$$ where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

A

$$\frac{3y}{2x (x + c)}$$

B

$$\frac{3y}{2c (x + c)}$$

C

$$\frac{3y}{4x (x + c)}$$

D

$$\frac{3y}{4c (x + c)}$$