568. Given the problem: "Through a point $C$, taken on the extension of the diameter $\boldsymbol{A} \boldsymbol{B}$ of a circle with radius $\boldsymbol{R}$, draw a secant such that the sum $A E^{2}+B D^{2}$ equals a given number $m^{2}$." By calling $C O=a$ and taking as the unknown $x$ the distance of the chord $D E$ from the center of the circle $O$, we obtain after rather complex calculations the equation

$$
16 \boldsymbol{R}^{2} x^{4}--16 \boldsymbol{R}^{2} x^{2}\left(a^{2}+\boldsymbol{R}^{2}\right)+16 a^{4} \boldsymbol{R}^{4}-a^{2}\left(4 \boldsymbol{R}^{2}-m^{2}\right)^{2}=0
$$

For which special case can this equation be quickly verified?
568. In the limiting case, if $\boldsymbol{C D E}$ is a tangent, then $m^{2}=4 \boldsymbol{R}^{2}$, so $x=\boldsymbol{R}$.