Distance from Chord to Circle Edge?

[tomadom]

I'm trying to work out how to calculate the height of each line from the chord to the edge of the circle (see below).
I know the length of the Chord. (the red line)
I know the radius of the circle.
I also know the height of the center of the chord to the edge of the circle (the green line)

What I want to do, is work out the length of the blue lines at any point along the chord. I'm building something and the radius of the circle is over 4 meters so I'm trying to work out another way of drawing the curve which is part of a larger circle. Thanks!

 

[tomadom]

tough question?

I'm assuming this is a tough question? I can't think of a way to do this? Maybe somebody has an idea how to approach such a problem?

 

[Dr.Peterson]

I'm assuming this is a tough question? I can't think of a way to do this? Maybe somebody has an idea how to approach such a problem?

No, it isn't particularly hard. Do you know the equation of a circle? Here, you are essentially asking for y as a function of x. Or, you can think in terms of the Pythagorean theorem.

Here is a discussion of essentially your problem, including a formula for y, in case you've forgotten that bit of algebra.

On the other hand, it's not really hard to make a circle with 4-meter radius; just use a 4-meter string (assuming there's enough space in your workshop).

 

[tomadom]

That's brilliant, thank you very much for this!
It's been a while since I've been to school but looking at this it's coming back to me.
It will be too difficult to use a string for this radius accurately so the formula method is a must.