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5 Comments

Let (x1,y1) and (x2,y2) be two of the points on arc.

Then :

(x-x1)^2+(y-y1)^2=r^2 where r is the radius.

(x-x2)^2+(y-y2)^2=r^2

So equate these two equations to get the centre of circle which (x,y)

With regards,

V.Kartik

Given any two points, there are an infinite number of different arcs that pass through both.

You can see this because if you do what kartik suggested, you get:

(x-x1)^2+(y-y1)^2=(x-x2)^2

1 equation with 2 unknowns (x and y) has an infinite number of solutions.

So you need *three* points, from which you can get *two* equations:

(x-x1)^2+(y-y1)^2=(x-x2)^2

and

(x-x1)^2+(y-y1)^2=(x-x3)^2

and now you really can solve for x and y.

kotan answered the question `how do I find the center of mass of the arc' rather than `how do I find the center of the circle of which the arc belongs to' .. if that was what you intended, then his answer is correct.

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