I need to find the right radius so my segment of a circle start and end on specifics coordinates.

For example: I got a segment that start at $[0,0]$ and I would like that it end at $[X=4750 / Y= -2000]$. For this example, I do know the length chord $= 5154$ (Pythagoras's theorem).

I tried something like this (see picture) but cannot isolate r... equation

Is it possible to find the radius? and how? Thanks for your help.


There are infinite circles that pass through two specific distinct points. Their centers lay along the chord perpendicular bisector. For example, one of the circles has its center at the midpoint of the chord and its radius is the length of the chord divided by two.

If you want to find a unique circle a third point is needed (not on the same line of the other two). You can do some experiments HERE. See also Get the equation of a circle when given 3 points


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