I don't know the proper terminology, or even how to draw the right diagram, but I'm looking to work out
a for any given
a= the thick, horizontal line, distance from
yto circle's edge
x= can be considered the x axis
y= can be considered the y axis
- pink line is the secant (I love Wikipedia)
a must get shorter, the further down
y it is drawn. The second, lower thick horizontal line
a shows this.
a (I know the radius of the circle) and I know the length of the second, lower line
a (because I know the distance along
x from the center to the pink line).
I want to find out
V, that is, a vector describing where the pink line bisects the circle. My idea is that (I'm a programmer not a mathematician) as line
a moves 'south' along
y, it must shorten according to some ratio or function of the radius of the circle.
a are related by some function of the radius. Probably.
If someone knows that function, then I can work out
y for any given
a. So knowing
x, I can then work out
y in terms of
x and arrive at
If someone has a better way to work out
V, then let me know. In real life, the pink line is at an angle, but I will rotate the entire coordinate space, work out
V and then rotate it back :)
Excuse my ignorance.