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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.

Explanatory image

Feel free to help me tag this appropriately.

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You are looking for $ED$? –  Babak S. Aug 4 '13 at 22:51
    
@BabakS. Yes, the distance between those two points. –  JohnWO Aug 5 '13 at 11:19

2 Answers 2

up vote 1 down vote accepted

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

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We can also assume that $CD$ is 2 on this diagram and that $CE=\frac{AB}2=CB=AC$ –  Alizter Aug 4 '13 at 22:57
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Sweet... Thanks for reminding me of this fundamental theorem! (It has been a VERY long while since I dabbled with geometry... Not since grade school, if I recall correctly...) This is what I ended up with: $DE = \sqrt{\left (\frac{AB}{2}\right )^2-CD^2}$. Again, thanks! –  JohnWO Aug 5 '13 at 11:33

there is this possibility too.

BD/DE=DE/AD

and DE²=BD*DA

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