Calculating position/distance of point on arc of circle

Question

I'm having a hard time trying to wrap my head around this problem.

Imagine a line of length $A+B$ with center $C$, with a circle with $d = A+B$ with center at $C$.
Now imagine drawing a line at $90^{\circ}$ from an arbitrary point, $D$, along the line $A+B$, which intersects the circle at point $E$.
How could one calculate the distance between $D$ and $E$ the point?

This is kinda hard to explain, as English is not my first language, so please refer to picture for an example.

Feel free to help me tag this appropriately.

Answer 1

Pithagora's theorem tells you that $$CD^2+DE^2 = \left(\frac{AB}{2}\right)^2$$

Answer 2

there is this possibility too.

BD/DE=DE/AD

and DE²=BD*DA