How Can I Find the Centre Point of a Circle with Given Coordinates and Radius?

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To find the center point of a circle given two points and a radius, the general equation for a circle in Cartesian coordinates can be used. This approach results in two simultaneous equations that need to be solved. While some users express a desire for a simplified formula for direct input into programming, the equations are manageable. The discussion emphasizes that although the calculations may seem cumbersome, they are not overly complex. Understanding the mathematical principles behind the equations is essential for accurate results.
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given the x,y coordinates of two points and the radius of a curve. has anyone got a formula for calculating the coordinates of the centre point please
 
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bikermart said:
given the x,y coordinates of two points and the radius of a curve. has anyone got a formula for calculating the coordinates of the centre point please
One can simply use the general equation for a circle in Cartesian coordinates.
 
which is ?
 
thats great thanks but that give me two simultaneous equations to work out.
i might be being lazy here but has anyone trawled out the formula such that given x1,y1,x2,y2 and r then a= and b= so i can just stick them in my program.
cheers.
 
bikermart said:
thats great thanks but that give me two simultaneous equations to work out.
Indeed it does. But they are not difficult.
 
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