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Coordinate of the point having same distance from three points in plane; center of a circle

작성자 Uploader : rainman 작성일 Upload Date: 2018-08-19변경일 Update Date: 2018-08-20조회수 View : 300

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Coordinate of the point having same distance from three points
(x1, y1), (x2, y2), (x3, y3) in plane;  center of a circle

Letting an arbitrary point having same distance as (x, y), its ddistancs from two points (x1, y1) and (x2, y2) are identical and rxpressed as:

((x-x1)^2 + (y-y1)^2) = ((x-x2)^2 + (y-y2)^2)

Rearranging,

y = (x1-x2)x/(y2-y1) + (x2^2 + y2^2 - x1^2 - y1^2)/(2(y2-y1))

Provided y1 ≠ y2, the above can be expressed as below:

y = Ax + B, A=(x1-x2)/(y2-y1), B=(x2^2 + y2^2 - x1^2 - y1^2)/(2(y2-y1))

Similarly, the distance from (x2, y2) and (x3, y3) is:

y = (x2-x3)x/(y3-y2) + (x3^2 + y3^2 - x2^2 - y2^2)/(2(y3-y2))  (but y2 ≠ y3)

y = Cx + D, C = (x2-x3)/(y3-y2), D= (x3^2 + y3^2 - x2^2 - y2^2)/(2(y3-y2))

Combining the above two equations,,

Ax + B = Cx + D

Then,

x = (D-B)/(A-C)

Note that the point (x, y) is the center of a circle on which those three points lie. 
◎ Input coordinates.


□ A, B, C, D








□ Center of the circle (x, y)




□ Distance from the points, i.e. radius of the circle (R)


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