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translate points along a line to points along a tangent line of a circle

hey

i'm new,

i have an out of school question (programming graphics for a game) , and unfortunately my memory / knowledge of geometry is very limited.

the question:

i have several points positioned along a horizontal line, like - (a,0), (b,0), (c,0), ...

i need to position the line (or collection of points) as a tangent to a circle at any given point, while preserving the distance between the points,

and get the new coordinates of each point.

the point (relative to the line) where the line touches the circle is (0,0)

the point on the circle varies

the circle's center is (0,0), radius of say, 10.

i have attached a drawing which might illustrate it a bit

any help would be very greatly appreciated

thanks,

michael